If the function $f: \mathbb{N} \rightarrow \mathbb{N}$ is defined as $f(n)=\left\{\begin{array}{ll}n-1, & \text { if } n \text { is even } \\ n+1, & \text { if } n \text { is odd }\end{array}\right.$, then (A) f is injective (B) f is into (C) f is surjective (D) f is invertible

Let $f : [2, \infty) \to \mathbf{R}$ be a function defined by $f(x) = x^2 - 4x + 5$. The range of $f$ is :

Let a relation R = {(a, b) : a is a factor of b, a, b $\in$ N}. Then, R is ______.

Let N be set of natural numbers, then the function $f: \mathbb{N} \rightarrow \mathbb{N}$, defined by

$f(x) = \begin{cases} \frac{n+1}{2} & \text{, if } n \text{ is odd} \\ \frac{n}{2} & \text{, if } n \text{ is even} \end{cases}$, is

If $n(A) = 3$, $n(B) = 2$, then number of all possible surjective function from set A to set B are :

Let $R : \mathbb{R} \to \mathbb{R}$, where $\mathbb{R}$ is the set of real numbers and R be a relation. An element $(x, y) \in R$ if $x + y - \sqrt{2}$ belongs to the set of irrational numbers. Then the relation R is :

Let a relation $R$ be defined on a set $A = \{1,2,3,4,5\}$ as $R = \{(a,b): |a-b| \text{ is even or zero}\}$. Then which of the following statements is not TRUE?