Assertion (A): A function f : N N be defined by f(n)= ll n 2 & if… - Vidyadip

MCQ

Assertion (A): A function $f : N \rightarrow N$ be defined by $f(n)=\left\{\begin{array}{ll}\frac{n}{2} & \text { if } n \text { is even } \\ \frac{(n+1)}{2} & \text { if } n \text { is odd }\end{array}\right.$ for all $n \in N$; is one-one
Reason (R): A function $f: A \rightarrow B$ is said to be injective if $a \neq b$ then $f(a) \neq f(b)$.

A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
✓
A is false but R is true.

✓

Answer

Correct option: D.

A is false but R is true.

(d) A is false but R is true.
Explanation: Assertion is false because distinct elements in N has equal images.
for example $f(1)=\frac{(1+1)}{2}=1$
$f(2)=\frac{2}{2}=1$
Reason is true because for injective function if elements are not equal then their images should be unequal.

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