LA

A relation R on set $A=\{-4,-3,-2,-1,0,1,2,3,4\}$ be defined as $R=\{(x,y):x+y$ is an integer divisible by 2). Show that R is an equivalence relation. Also, write the equivalence class [2].

VSA

Check whether $f:R-\{3\} \rightarrow R$ defined as $f(x)=\frac{x-2}{x-3}$ is onto or not.

VSA

Check whether $f : Z \times Z \to Z \times Z$ (where $Z$ is the set of integers) defined as $f(x, y) = (2y, 3x)$ is injective or not. [Delhi 2026]

SA

Show that the function $f:N\rightarrow N$, where N is a set of natural numbers, given by $f(n) = n-1$, if n is even, $n+1$, if n is odd, is a bijection.

VSA

Consider the relation $\phi$ on a non-empty set $A$. Then, check whether $R$ is symmetric, reflexive or transitive.

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