# 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 ... 373 views 1 answers What is direct marketing? 709 views 1 answers How might aggressive direct marketing affect public relations? 299 views 1 answers How can public relations be used by Ford and Firestone following investigations into complaints about tire failures? 365 views 0 answers 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 !... 670 views 1 answers 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... 348 views 1 answers 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{... 394 views 1 answers 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(... 431 views 1 answers 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)... 439 views 1 answers 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...