SA

Check whether the relation $R$ in $R$ defined by $R = \{(a, b) : a \le b^3\}$ is reflexive, symmetric or transitive. [All India 2024]

LA

Let $R$ be relation defined on the set of natural number $N$ as follows, $R = \{(x, y) : x \in N, y \in N, 2x + y = 41\}$. Find the domain and range of the relation $R$. Also verify whether $R$ is reflexive, symmetric and transitive. [Exemplar]

VSA

A function $f : A \to B$ defined as $f(x) = 2x$ is both one-one and onto. If $A = \{1, 2, 3, 4\}$, then find the set $B$. [All India 2024]

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].

SA

Let R be a relation defined on a set N of natural numbers such that $R=\{(x,y): xy \text{ is a square of a natural number, } x, y\in N\}$. Determine if the relation R is an equivalence relation.

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