MathsGee Answers - Recent questions tagged set
https://mathsgee.com/tag/set
Powered by Question2AnswerWhat are complex conjugates?
https://mathsgee.com/30080/what-are-complex-conjugates
What are complex conjugates?Mathematicshttps://mathsgee.com/30080/what-are-complex-conjugatesSat, 19 Jun 2021 01:40:47 +0000How are complex numbers related to real numbers?
https://mathsgee.com/30078/how-are-complex-numbers-related-to-real-numbers
How are complex numbers related to real numbers?Mathematicshttps://mathsgee.com/30078/how-are-complex-numbers-related-to-real-numbersSat, 19 Jun 2021 01:39:10 +0000Find the area of the shaded triangle if the area of an equilateral triangle $\triangle A B C$ is 36
https://mathsgee.com/29941/find-area-shaded-triangle-area-equilateral-triangle-triangle
<p>Find the area of the shaded triangle if the area of an equilateral triangle $\triangle A B C$ is 36</p>
<p><img alt="" src="https://mathsgee.com/?qa=blob&qa_blobid=9192212372798176632"></p>Mathematicshttps://mathsgee.com/29941/find-area-shaded-triangle-area-equilateral-triangle-triangleWed, 16 Jun 2021 09:02:18 +0000Points $A(-3,2)$ and $B(1,4)$ are end points of the diameter of the circle. The equation of the circle is:
https://mathsgee.com/29905/points-and-are-end-points-diameter-circle-equation-the-circle
Points $A(-3,2)$ and $B(1,4)$ are end points of the diameter of the circle. The equation of the circle is:Mathematicshttps://mathsgee.com/29905/points-and-are-end-points-diameter-circle-equation-the-circleWed, 16 Jun 2021 08:23:19 +0000One of the solutions of equation $z^{3}=w$ is $z_{1}=-5 \sqrt{3}+5 i$. What is one of other two solutions if $w$ is a complex number?
https://mathsgee.com/29895/solutions-equation-sqrt-what-other-solutions-complex-number
One of the solutions of equation $z^{3}=w$ is $z_{1}=-5 \sqrt{3}+5 i$. What is one of other two solutions if $w$ is a complex number?Mathematicshttps://mathsgee.com/29895/solutions-equation-sqrt-what-other-solutions-complex-numberWed, 16 Jun 2021 08:14:41 +0000If $\alpha$ and $\beta$ are the roots of the equation $x^{2}-x+1=0$, then $\alpha^{2009}+\beta^{2009}=$
https://mathsgee.com/29731/alpha-and-beta-are-roots-equation-then-alpha-2009-beta-2009
If $\alpha$ and $\beta$ are the roots of the equation $x^{2}-x+1=0$, then $\alpha^{2009}+\beta^{2009}=$<br />
<br />
1) $-1$<br />
2) 1<br />
3) 2<br />
4) $-2$Mathematicshttps://mathsgee.com/29731/alpha-and-beta-are-roots-equation-then-alpha-2009-beta-2009Sat, 12 Jun 2021 05:05:17 +0000Classify the numbers as members of the following set or sets:
https://mathsgee.com/29704/classify-the-numbers-as-members-of-the-following-set-or-sets
Classify the numbers as members of the following set or sets:<br />
$\begin{array}{llll}\text { A. Natural Numbers } & \text { B. Whole Numbers } & \text { C. Integers } & \text { D. Rationals } & \text { E. Irrationals }\end{array}$<br />
$$<br />
\pi,-3,1 / 3, \sqrt{6}, 0,2,0 . \overline{3},-1 / 9,100, \sqrt{7}<br />
$$Mathematicshttps://mathsgee.com/29704/classify-the-numbers-as-members-of-the-following-set-or-setsFri, 11 Jun 2021 06:56:05 +0000Let two numbers have arithmetic mean 9 and geometric mean $4 .$ Then these numbers are the roots of the quadratic equation
https://mathsgee.com/29539/numbers-arithmetic-geometric-numbers-quadratic-equation
Let two numbers have arithmetic mean 9 and geometric mean $4 .$ Then these numbers are the roots of the quadratic equation<br />
<br />
1) $x^{2}+18 x+16=0$<br />
2) $x^{2}-18 x-16=0$<br />
3) $x^{2}+18 x-16=0$<br />
4) $x^{2}-18 x+16=0$Mathematicshttps://mathsgee.com/29539/numbers-arithmetic-geometric-numbers-quadratic-equationWed, 09 Jun 2021 07:22:59 +0000If $\alpha \neq \beta$ but $\alpha^{2}=5 \alpha-3$ and $\beta^{2}=5 \beta-3$ then the equation having $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$ as its roots is
https://mathsgee.com/29523/alpha-beta-alpha-alpha-equation-having-alpha-frac-alpha-roots
If $\alpha \neq \beta$ but $\alpha^{2}=5 \alpha-3$ and $\beta^{2}=5 \beta-3$ then the equation having $\dfrac{\alpha}{\beta}$ and $\dfrac{\beta}{\alpha}$ as its roots is<br />
<br />
1) $3 x^{2}-19 x+3=0$<br />
2) $3 x^{2}+19 x-3=0$<br />
3) $3 x^{2}-19 x-3=0$<br />
4) $x^{2}-5 x+3=0$Mathematicshttps://mathsgee.com/29523/alpha-beta-alpha-alpha-equation-having-alpha-frac-alpha-rootsWed, 09 Jun 2021 06:58:48 +0000If $z \neq 1$ and $\frac{z^{2}}{z-1}$ is real, then the point represented by the complex number $\mathrm{z}$ lies
https://mathsgee.com/29521/frac-real-then-point-represented-complex-number-mathrm-lies
If $z \neq 1$ and $\frac{z^{2}}{z-1}$ is real, then the point represented by the complex number $\mathrm{z}$ lies<br />
<br />
1) either on the real axis or on a circle not passing through the origin<br />
2) on a circle with centre at the origin<br />
3) either on the real axis or on a circle not passing through the origin.<br />
4) on the imaginary axisMathematicshttps://mathsgee.com/29521/frac-real-then-point-represented-complex-number-mathrm-liesWed, 09 Jun 2021 06:55:37 +0000Let $\alpha, \beta$ be real and $z$ be a complex number. If $z^{2}+\alpha z+\beta=0$ has two distinct roots on the line $\operatorname{Re} z=1$, then it is necessary that
https://mathsgee.com/29517/alpha-beta-complex-number-distinct-operatorname-necessary
Let $\alpha, \beta$ be real and $z$ be a complex number. If $z^{2}+\alpha z+\beta=0$ has two distinct roots on the<br />
line $\operatorname{Re} z=1$, then it is necessary that<br />
<br />
1) $|\beta|=1$<br />
2) $\beta \in(1, \infty)$<br />
3) $\beta \in(0,1)$<br />
4) $\beta \in(-1,0)$Mathematicshttps://mathsgee.com/29517/alpha-beta-complex-number-distinct-operatorname-necessaryWed, 09 Jun 2021 06:48:42 +0000The number of complex number $z$ such that $|z-1|=|z+1|=|z-i|$ equals
https://mathsgee.com/29515/the-number-of-complex-number-z-such-that-z-1-z-1-z-i-equals
The number of complex number $z$ such that $|z-1|=|z+1|=|z-i|$ equals<br />
<br />
1) 1<br />
2) 2<br />
3) $\infty$<br />
4) 0Mathematicshttps://mathsgee.com/29515/the-number-of-complex-number-z-such-that-z-1-z-1-z-i-equalsWed, 09 Jun 2021 06:46:27 +0000Let $A$ and $B$ denote the statements $A: \cos \alpha+\cos \beta+\cos \gamma=0$ $B: \sin \alpha+\sin \beta+\sin \gamma=0$
https://mathsgee.com/29511/denote-statements-alpha-beta-gamma-alpha-sin-beta-sin-gamma
Let $A$ and $B$ denote the statements<br />
<br />
$A: \cos \alpha+\cos \beta+\cos \gamma=0$<br />
$B: \sin \alpha+\sin \beta+\sin \gamma=0$<br />
<br />
If $\cos (\boldsymbol{\beta}-\gamma)+\cos (\gamma-\alpha)+\cos (\alpha-\beta)=-\frac{3}{2}$, then<br />
<br />
1) $\mathrm{A}$ is true and $\mathrm{B}$ is false<br />
2) $\mathrm{A}$ is false and $\mathrm{B}$ is true<br />
3) both $\mathrm{A}$ and $\mathrm{B}$ are true<br />
4) both $\mathrm{A}$ and $\mathrm{B}$ are falseMathematicshttps://mathsgee.com/29511/denote-statements-alpha-beta-gamma-alpha-sin-beta-sin-gammaWed, 09 Jun 2021 06:42:34 +0000If $z^{2}+z+1=0$, where $z$ is a complex number, then the value of
https://mathsgee.com/29505/if-z-2-z-1-0-where-z-is-a-complex-number-then-the-value-of
If $z^{2}+z+1=0$, where $z$ is a complex number, then the value of<br />
<br />
$\begin{aligned}\left(z+\frac{1}{z}\right)^{2}+\left(z^{2}+\frac{1}{z^{2}}\right)^{2}+\left(z^{3}+\frac{1}{z^{3}}\right)^{2}+\\ \ldots .+\left(z^{6}+\frac{1}{z^{6}}\right)^{2} & \text { is } \end{aligned}$<br />
<br />
1) 18<br />
2) 54<br />
3) 6<br />
4) 12Mathematicshttps://mathsgee.com/29505/if-z-2-z-1-0-where-z-is-a-complex-number-then-the-value-ofWed, 09 Jun 2021 06:36:54 +0000If $z_{1}$ and $z_{2}$ are two non-zero complex numbers such that $\left|z_{1}+z_{2}\right|=\left|z_{1}\right|+\left|z_{2}\right|$ then $\arg z_{1}-\arg z_{2}$ is equal to
https://mathsgee.com/29499/complex-numbers-left-right-left-right-left-right-then-equal
If $z_{1}$ and $z_{2}$ are two non-zero complex numbers such that $\left|z_{1}+z_{2}\right|=\left|z_{1}\right|+\left|z_{2}\right|$ then $\arg z_{1}-\arg z_{2}$ is equal to <br />
<br />
1) $\frac{\pi}{2}$<br />
2) $-\pi$<br />
3) 0<br />
4) $-\frac{\pi}{2}$Mathematicshttps://mathsgee.com/29499/complex-numbers-left-right-left-right-left-right-then-equalWed, 09 Jun 2021 06:30:08 +0000Let $z, w$ be complex numbers such that $\bar{z}+i \bar{w}=0$ and $\arg z w=\pi .$ Then arg $z$ equals
https://mathsgee.com/29491/let-complex-numbers-such-that-bar-and-arg-then-arg-z-equals
Let $z, w$ be complex numbers such that $\bar{z}+i \bar{w}=0$ and $\arg z w=\pi .$ Then arg $z$ equals<br />
<br />
1) $\frac{\pi}{4}$<br />
2) $\frac{5 \pi}{4}$<br />
3) $\frac{3 \pi}{4}$<br />
4) $\frac{\pi}{2}$Mathematicshttps://mathsgee.com/29491/let-complex-numbers-such-that-bar-and-arg-then-arg-z-equalsWed, 09 Jun 2021 05:41:06 +0000If $z$ and $w$ are two non-zero complex numbers such that $|z w|=1$, and $\operatorname{Arg}(z)-\operatorname{Arg}(w)=\frac{\pi}{2}$, then $\bar{z} \omega$ is equal to
https://mathsgee.com/29487/complex-numbers-operatorname-operatorname-then-omega-equal
If $z$ and $w$ are two non-zero complex numbers such that $|z w|=1$, and $\operatorname{Arg}(z)-\operatorname{Arg}(w)=\dfrac{\pi}{2}$, then $\bar{z} \omega$ is equal to<br />
<br />
1) 1<br />
2) $-1$<br />
3) $i$<br />
4) $-i$Mathematicshttps://mathsgee.com/29487/complex-numbers-operatorname-operatorname-then-omega-equalWed, 09 Jun 2021 05:37:16 +0000Let $z_{1}$ and $z_{2}$ be two roots of the equation $z^{2}+a z+b=0, z$ being complex. Further, assume that the origin, $z_{1}$ and $z_{2}$ form an equilateral triangle, then
https://mathsgee.com/29485/equation-complex-further-assume-origin-equilateral-triangle
Let $z_{1}$ and $z_{2}$ be two roots of the equation $z^{2}+a z+b=0, z$ being complex. Further, assume that the origin, $z_{1}$ and $z_{2}$ form an equilateral triangle, then <br />
<br />
1) $a^{2}=b$<br />
2) $a^{2}=2 b$<br />
3) $a^{2}=3 b$<br />
4) $a^{2}=4 b$Mathematicshttps://mathsgee.com/29485/equation-complex-further-assume-origin-equilateral-triangleWed, 09 Jun 2021 05:35:25 +0000The locus of the centre of a circle which touches the circle $\left|z-z_{1}\right|=a$ and $\left|z-z_{2}\right|=b$ externally $\left(z, z_{1}\right.$ and $z_{2}$ are complex numbers) will be
https://mathsgee.com/29483/centre-circle-touches-circle-externally-right-complex-numbers
The locus of the centre of a circle which touches the circle $\left|z-z_{1}\right|=a$ and $\left|z-z_{2}\right|=b$ externally $\left(z, z_{1}\right.$ and $z_{2}$ are complex numbers) will be<br />
<br />
1) an ellipse<br />
2) a hyperbola<br />
3) a circle<br />
4) none of theseMathematicshttps://mathsgee.com/29483/centre-circle-touches-circle-externally-right-complex-numbersWed, 09 Jun 2021 05:33:31 +0000If $|z-4|<|z-2|$, its solution is given by
https://mathsgee.com/29481/if-z-4-z-2-its-solution-is-given-by
If $|z-4|<|z-2|$, its solution is given by<br />
<br />
1) $\operatorname{Re}(z)>0$<br />
2) $\operatorname{Re}(z)<0$<br />
3) $\operatorname{Re}(z)>3$<br />
4) $\operatorname{Re}(z)>2$Mathematicshttps://mathsgee.com/29481/if-z-4-z-2-its-solution-is-given-byWed, 09 Jun 2021 05:31:51 +0000$z$ and $w$ are two non zero complex no.s such that $|z|=|w|$ and $\operatorname{Arg} z+A r g w=\pi$ then $z$ equals
https://mathsgee.com/29479/and-zero-complex-such-that-operatorname-pi-then-z-equals
$z$ and $w$ are two non zero complex no.s such that $|z|=|w|$ and $\operatorname{Arg} z+A r g w=\pi$ then $z$ equals<br />
<br />
1) $\bar{w}$<br />
2) $-\bar{w}$<br />
3) w<br />
4) $-w$Mathematicshttps://mathsgee.com/29479/and-zero-complex-such-that-operatorname-pi-then-z-equalsWed, 09 Jun 2021 05:28:37 +0000Let $\mathbf{x}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, 5\} .$ The number of different ordered pairs. $(\mathbf{y}, \mathbf{z})$ that can be formed such that $Y \in X, Z \in X$ and $y \cap z$ is empty, is
https://mathsgee.com/29477/mathbf-mathbf-number-different-ordered-mathbf-mathbf-formed
Let $\mathbf{x}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, 5\} .$ The number of different ordered pairs. $(\mathbf{y}, \mathbf{z})$ that can be formed such that $Y \in X, Z \in X$ and $y \cap z$ is empty, is<br />
<br />
1) $5^{2}$<br />
2) $3^{5}$<br />
3) $2^{3}$<br />
4) $5^{3}$Mathematicshttps://mathsgee.com/29477/mathbf-mathbf-number-different-ordered-mathbf-mathbf-formedWed, 09 Jun 2021 05:25:27 +0000Let $R$ be the set of real numbers Statement-1 : $A=\{(x, y) \in R \times R: y-x$ is an integer $\}$ is an equivalence relation on $\mathbf{R}$ Statement-2 : $B=\{(x, y) \in R \times R: x=\alpha y$ for
https://mathsgee.com/29471/numbers-statement-integer-equivalence-relation-statement
Let $R$ be the set of real numbers Statement-1 : $A=\{(x, y) \in R \times R: y-x$ is an integer $\}$ is an equivalence relation on $\mathbf{R}$ Statement-2 : $B=\{(x, y) \in R \times R: x=\alpha y$ for<br />
some rational number $\alpha\}$ is an equivalence relation of $\mathbf{R}$.<br />
<br />
1) Statement- 1 is true, Statement- 2 is false<br />
2) Statement-1 is false, Statement- 2 is true<br />
3) Statement-1 is true, Statement- 2 is true; Statement- 2 is a correct explanation for Statement-1<br />
4) Statement- 1 is true, Statement 2 is true; Statement- 2 is not a correct explanation for Statement-1Mathematicshttps://mathsgee.com/29471/numbers-statement-integer-equivalence-relation-statementWed, 09 Jun 2021 05:19:33 +0000If $A, B$ and $C$ are three sets such that $A \cap B=A \cap C$ and $A \cup B=A \cup C$, then
https://mathsgee.com/29459/if-and-c-are-three-sets-such-that-cap-cap-and-a-cup-cup-c-then
If $A, B$ and $C$ are three sets such that $A \cap B=A \cap C$ and $A \cup B=A \cup C$, then<br />
<br />
1) $A=B$<br />
2) $A=C$<br />
3) $B=C$<br />
4) $A \cap B=\phi$.Mathematicshttps://mathsgee.com/29459/if-and-c-are-three-sets-such-that-cap-cap-and-a-cup-cup-c-thenWed, 09 Jun 2021 04:07:27 +0000Let $\mathbf{R}=\{(3,3),(6,6),(9,9),(12,12),(6,12),$, $(3,9),(3,12),(3,6)\}$ be a relation on the set $A=\{3,6,9,12\}$ be a relation on the set $A=\{3,6,9,12\} .$ The relation is
https://mathsgee.com/29441/let-mathbf-12-relation-the-set-relation-the-set-the-relation
Let $\mathbf{R}=\{(3,3),(6,6),(9,9),(12,12),(6,12),$, $(3,9),(3,12),(3,6)\}$ be a relation on the set $A=\{3,6,9,12\}$ be a relation on the set $A=\{3,6,9,12\} .$ The relation is<br />
<br />
1) reflexive and transitive only<br />
2) reflexive only<br />
3) an equivalence relation<br />
4) reflexive and symmetric onlyMathematicshttps://mathsgee.com/29441/let-mathbf-12-relation-the-set-relation-the-set-the-relationWed, 09 Jun 2021 03:45:29 +0000Let $A$ and $B$ be metric spaces, and let $f: A \rightarrow B$. Suppose that whenever $X$ is an open set in $B$, the set $\{a \in A: f(a) \notin X\}$ is closed in $A .$ Which of the following must be true?
https://mathsgee.com/29008/metric-spaces-rightarrow-suppose-whenever-closed-following
Let $A$ and $B$ be metric spaces, and let $f: A \rightarrow B$. Suppose that whenever $X$ is an open set in $B$, the set $\{a \in A: f(a) \notin X\}$ is closed in $A .$ Which of the following must be true?<br />
<br />
I. $f$ is injective.<br />
II. $f$ is continuous.<br />
III. $f$ is a homeomorphism.<br />
<br />
(A) None<br />
(B) II only<br />
(C) III only<br />
(D) I and III only<br />
(E) I, II, and IIIMathematicshttps://mathsgee.com/29008/metric-spaces-rightarrow-suppose-whenever-closed-followingSat, 29 May 2021 23:25:58 +0000Solve the following quadratic inequality. Write the solution set in interval notation. $$ x^{2}-2 x-35<0 $$
https://mathsgee.com/28985/following-quadratic-inequality-solution-interval-notation
Solve the following quadratic inequality. Write the solution set in interval notation.<br />
$$<br />
x^{2}-2 x-35<0<br />
$$Mathematicshttps://mathsgee.com/28985/following-quadratic-inequality-solution-interval-notationSat, 29 May 2021 22:54:53 +0000Solve the following inequality. Write the solution set in interval notation. $$ 2 \geq \frac{5-3 x}{4}>-3 $$
https://mathsgee.com/28984/solve-following-inequality-write-solution-interval-notation
Solve the following inequality. Write the solution set in interval notation.<br />
$$<br />
2 \geq \frac{5-3 x}{4}>-3<br />
$$Mathematicshttps://mathsgee.com/28984/solve-following-inequality-write-solution-interval-notationSat, 29 May 2021 22:54:07 +0000What are equivalence classes in set theory?
https://mathsgee.com/28921/what-are-equivalence-classes-in-set-theory
What are equivalence classes in set theory?Mathematicshttps://mathsgee.com/28921/what-are-equivalence-classes-in-set-theoryThu, 27 May 2021 22:31:09 +0000What are equivalence relations in set theory?
https://mathsgee.com/28919/what-are-equivalence-relations-in-set-theory
What are equivalence relations in set theory?Mathematicshttps://mathsgee.com/28919/what-are-equivalence-relations-in-set-theoryThu, 27 May 2021 22:27:05 +0000What are the basic set operations?
https://mathsgee.com/28917/what-are-the-basic-set-operations
What are the basic set operations?Mathematicshttps://mathsgee.com/28917/what-are-the-basic-set-operationsThu, 27 May 2021 22:25:15 +0000Using the axioms of probability, prove the following:
https://mathsgee.com/28618/using-the-axioms-of-probability-prove-the-following
Using the axioms of probability, prove the following:<br />
<br />
a. For any event $A, P\left(A^{c}\right)=1-P(A)$.<br />
b. The probability of the empty set is zero, i.e., $P(\emptyset)=0$.<br />
c. For any event $A$, $P(A) \leq 1$.<br />
d. $P(A-B)=P(A)-P(A \cap B)$.<br />
e. $P(A \cup B)=P(A)+P(B)-P(A \cap B)$, (inclusion-exclusion principle for $n=2$ ).<br />
f. If $A \subset B$ then $P(A) \leq P(B)$.Data Science & Statisticshttps://mathsgee.com/28618/using-the-axioms-of-probability-prove-the-followingSat, 22 May 2021 09:55:20 +0000Let $S=\{1,2,3\}$. Write all the possible partitions of $S$.
https://mathsgee.com/28602/let-s-1-2-3-write-all-the-possible-partitions-of-s
Let $S=\{1,2,3\}$. Write all the possible partitions of $S$.Mathematicshttps://mathsgee.com/28602/let-s-1-2-3-write-all-the-possible-partitions-of-sSat, 22 May 2021 06:59:39 +0000Prove that any subset of a countable set is countable and any superset of an uncountable set is uncountable.
https://mathsgee.com/28594/subset-countable-countable-superset-uncountable-uncountable
Prove that any subset of a countable set is countable and any superset of an uncountable set is uncountable.Mathematicshttps://mathsgee.com/28594/subset-countable-countable-superset-uncountable-uncountableSat, 22 May 2021 06:44:23 +0000Are there any guidelines for deciding whether an infinite set is countable or not?
https://mathsgee.com/28592/are-there-guidelines-deciding-whether-infinite-countable
Are there any guidelines for deciding whether an infinite set is countable or not?Mathematicshttps://mathsgee.com/28592/are-there-guidelines-deciding-whether-infinite-countableSat, 22 May 2021 06:40:02 +0000How do I determine the cardinality of a finite set?
https://mathsgee.com/28584/how-do-i-determine-the-cardinality-of-a-finite-set
How do I determine the cardinality of a finite set?Mathematicshttps://mathsgee.com/28584/how-do-i-determine-the-cardinality-of-a-finite-setSat, 22 May 2021 06:20:02 +0000What is the definition of cardinality of a set?
https://mathsgee.com/28582/what-is-the-definition-of-cardinality-of-a-set
What is the definition of cardinality of a set?Mathematicshttps://mathsgee.com/28582/what-is-the-definition-of-cardinality-of-a-setSat, 22 May 2021 06:18:11 +0000What is the multiplication principle in set theory?
https://mathsgee.com/28580/what-is-the-multiplication-principle-in-set-theory
What is the multiplication principle in set theory?Mathematicshttps://mathsgee.com/28580/what-is-the-multiplication-principle-in-set-theorySat, 22 May 2021 06:15:54 +0000If the universal set is given by $S=\{1,2,3,4,5,6\}$, and $A=\{1,2\}, B=\{2,4,5\}, C=\{1,5,6\}$ are three sets, find the following sets:
https://mathsgee.com/28576/universal-set-given-and-are-three-sets-find-the-following-sets
If the universal set is given by $S=\{1,2,3,4,5,6\}$, and $A=\{1,2\}, B=\{2,4,5\}, C=\{1,5,6\}$ are three sets, find the following sets:<br />
<br />
a. $A \cup B$<br />
b. $A \cap B$<br />
c. $\bar{A}$<br />
d. $\bar{B}$<br />
e. Check De Morgan's law by finding $(A \cup B)^{c}$ and $A^{c} \cap B^{c}$.<br />
f. Check the distributive law by finding $A \cap(B \cup C)$ and $(A \cap B) \cup(A \cap C)$.Mathematicshttps://mathsgee.com/28576/universal-set-given-and-are-three-sets-find-the-following-setsSat, 22 May 2021 06:12:11 +0000What is the distributive law in set theory?
https://mathsgee.com/28574/what-is-the-distributive-law-in-set-theory
What is the distributive law in set theory?Mathematicshttps://mathsgee.com/28574/what-is-the-distributive-law-in-set-theorySat, 22 May 2021 06:09:54 +0000What is a partition of a set A?
https://mathsgee.com/28570/what-is-a-partition-of-a-set-a
What is a partition of a set A?Mathematicshttps://mathsgee.com/28570/what-is-a-partition-of-a-set-aSat, 22 May 2021 06:06:36 +0000What is the complement of a set A?
https://mathsgee.com/28564/what-is-the-complement-of-a-set-a
What is the complement of a set A?Mathematicshttps://mathsgee.com/28564/what-is-the-complement-of-a-set-aSat, 22 May 2021 06:01:12 +0000What is a Universal Set in set theory?
https://mathsgee.com/28552/what-is-a-universal-set-in-set-theory
What is a Universal Set in set theory?Mathematicshttps://mathsgee.com/28552/what-is-a-universal-set-in-set-theorySat, 22 May 2021 05:45:36 +0000When is set A equal to set B in mathematics?
https://mathsgee.com/28550/when-is-set-a-equal-to-set-b-in-mathematics
When is set A equal to set B in mathematics?Mathematicshttps://mathsgee.com/28550/when-is-set-a-equal-to-set-b-in-mathematicsSat, 22 May 2021 05:43:15 +0000When is set A, a subset of set B?
https://mathsgee.com/28548/when-is-set-a-a-subset-of-set-b
When is set A, a subset of set B?Mathematicshttps://mathsgee.com/28548/when-is-set-a-a-subset-of-set-bSat, 22 May 2021 05:40:31 +0000What is a set in mathematics?
https://mathsgee.com/28542/what-is-a-set-in-mathematics
What is a set in mathematics?Mathematicshttps://mathsgee.com/28542/what-is-a-set-in-mathematicsSat, 22 May 2021 05:33:26 +0000The set of all possible outcomes is called
https://mathsgee.com/28139/the-set-of-all-possible-outcomes-is-called
The set of all possible outcomes is calledData Science & Statisticshttps://mathsgee.com/28139/the-set-of-all-possible-outcomes-is-calledThu, 13 May 2021 06:58:55 +0000Show that $$ \tan \left(z_{1}+z_{2}\right)=\frac{\tan z_{1}+\tan z_{2}}{1-\left(\tan z_{1}\right)\left(\tan z_{2}\right)} $$
https://mathsgee.com/27920/show-that-left-right-frac-tan-tan-left-tan-right-left-tan-right
Show that<br />
$$<br />
\tan \left(z_{1}+z_{2}\right)=\frac{\tan z_{1}+\tan z_{2}}{1-\left(\tan z_{1}\right)\left(\tan z_{2}\right)}<br />
$$<br />
for all complex numbers $z_{1}$ and $z_{2}$ satisfying $z_{1}, z_{2}, z_{1}+z_{2} \neq n \pi+\pi / 2$ for any integer<br />
$n$Mathematicshttps://mathsgee.com/27920/show-that-left-right-frac-tan-tan-left-tan-right-left-tan-rightMon, 10 May 2021 07:35:57 +0000Suppose $p(z)$ is a polynomial with real coefficients. Prove that
https://mathsgee.com/27910/suppose-p-is-polynomial-with-real-coefficients-prove-that
Suppose $p(z)$ is a polynomial with real coefficients. Prove that<br />
(a) $\overline{p(z)}=p(\bar{z})$;<br />
(b) $p(z)=0$ if and only if $p(\bar{z})=0$;<br />
(c) the roots of $p(z)=0$ appear in conjugate pairs, i.e., if $z_{0}$ is a root of $p(z)=0$, so is $\bar{z}_{0}$.Mathematicshttps://mathsgee.com/27910/suppose-p-is-polynomial-with-real-coefficients-prove-thatMon, 10 May 2021 07:13:35 +0000Show that $$ \left|z_{1}-z_{2}\right|^{2}+\left|z_{1}+z_{2}\right|^{2}=2\left(\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2}\right) $$ for all $z_{1}, z_{2} \in \mathbb{C}$.
https://mathsgee.com/27882/show-left-right-left-right-left-right-left-right-right-mathbb
Show that<br />
$$<br />
\left|z_{1}-z_{2}\right|^{2}+\left|z_{1}+z_{2}\right|^{2}=2\left(\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2}\right)<br />
$$<br />
for all $z_{1}, z_{2} \in \mathbb{C}$.Mathematicshttps://mathsgee.com/27882/show-left-right-left-right-left-right-left-right-right-mathbbMon, 10 May 2021 06:24:28 +0000