Recent questions tagged relations

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What sub-departments fall under UJ's university relations?
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How is congruence used in geometry?
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Is congruence an equivalence relation?
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Why are relations that define relationships among elements of a set or several sets important?
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How are equivalence relations used in mathematics?
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What are the properties of an equivalence relation?
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What is an equivalence relation in mathematics?
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Are one-to-many relations considered as functions?
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Prove the following limit relations:(a) \(\lim _{x \rightarrow 0} \frac{b^{x}-1}{x}=\log b \quad(b>0)\).(b) \(\lim _{x \rightarrow 0} \frac{\log (1+x)}{x}=1\).(c) \(\lim ...
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What is direct marketing?
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How might aggressive direct marketing affect public relations?
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How can public relations be used by Ford and Firestone following investigations into complaints about tire failures?
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For positive integers \(x\) and \(y\), find the largest \(x\) that satisfies\[y !(y-1) !=x !\]
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Determine the domain of \(y=\log _{9}(8 x+5)\).
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Determine the domain of \(y=\log _{7}(3 x-1)\).
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What are economic relations between and within nations?
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When is a real-valued function continuous?
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If $f(x)=x^{n}$, then the value of$$f(1)-\frac{f^{\prime}(1)}{1 !}+\frac{f^{\prime \prime}(1)}{2 !}-\frac{f^{\prime \prime}(1)}{3 !}+\ldots .+\frac{(-1)^{n} f^{n}(1)}{n !...
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Consider the following relations :$R=\{(x, y) \mid x, y$ are real numbers an $x=w y$ for some rational number $\mathbf{w}\}$; $S=\left\{\left(\frac{m}{n}, \frac{p}{q}\rig...
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A real valued function $f(x)$ satisfies the functional equation $\quad f(x-y)=f(x) f(y)-$ $f(a-x) f(a+y)$ where a is a given constant and $\mathbf{f}(\mathbf{0})=\mathbf{...
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Domain of definition of the function $f(x)=\dfrac{3}{4-x^{2}}+\log _{10}\left(x^{3}-x\right)$, is1) $(1,2)$2) $(-1,0) \cup(1,2)$3) $(1,2) \cup(2, \infty)$4) $(-1,0) \cup(...
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If $f: R \rightarrow R$ satisfies $f(x+y)=f(x)+f(y)$, for all $x, y \in R$ and $f(1)=7$, then $\sum_{r=1}^{n} f(r)$ is1) $\frac{7 n}{2}$2) $\frac{7(n+1)}{2}$3) $7 n(n+1)$...
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A function $f$ from the set of natural numbers to integers defined by $$f(n)=\left\{\begin{array}{l}\frac{n-1}{2}, \quad \text { when } n \text { is odd } \\ -\frac{n}{2}...
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The domain of $\sin ^{-1}\left[\log _{3}(x / 3)\right]$ is1) $[1,9]$2) $[-1,9]$3) $[-9,1]$4) $[-9,-1]$.
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Lemma: Let $\sim$ be an equivalence relation on A for $\forall^{\prime} a, b \in A$. Then either $\operatorname{cl}(a) \cap \operatorname{cl}(b)=\emptyset$ or $c l(a)=\op...
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What are equivalence classes in set theory?
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What are equivalence relations in set theory?
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