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.

SA

Let $A$ and $B$ be sets. Show that $f : A \times B \to B \times A$ such that $f(a, b) = (b, a)$ is bijective function. [NCERT]

SA

A relation R on set $A=\{1,2,3,4,5\}$ is defined as $R=\{(x,y):|x^{2}-y^{2}|

VSA

Let $R = \{(a, a^3) : a \text{ is a prime number less than } 5\}$ be a relation. Find the range of $R$. [All India 2014]

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]

View All Questions