VSA

A relation R on $A=\{1,2,3\}$ is defined as $R=\{(1,1),(3,3),(1,2)\}$. Is R a symmetric relation? Justify. Write the smallest relation set $R_{1}$ such that $R\cup R_{1}$ becomes an equivalence relation on the set {1, 2, 3}.

LA

Show that a function $f:\mathbb{R}\rightarrow\mathbb{R}$ defined as $f(x)=\frac{5x-3}{4}$ is both one-one and onto.

LA

A function $f : R - \{-1, 1\} \to R$ is defined by: $f(x) = \frac{x}{x^2 - 1}$. (i) Check if $f$ is one-one. (ii) Check if $f$ is onto. Show your work.

VSA

Find the maximum number of equivalence relations on the set $A = \{1, 2, 3\}$.

VSA

Let $R$ be a relation on the set $N$ be defined by $\{(x, y) : x, y \in N, 2x + y = 41\}$. Check whether $R$ is symmetric, reflexive or transitive.

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