question_answer

Assertion: A function \[f\,\,:\,\,N\,\,\to N\]be defined by

Reason: A function \[f\,\,:\,\,A\to B\]is said to be injective if \[f\left( a \right)=f\left( b \right)\Rightarrow a=b\].

A) Both A and R are individually true and R is the correct explanation of A.

B) Both A and R are individually true and R is not the correct explanation of A.

C) 'A' is true but 'R' is false

D) 'A' is false but 'R' is true

E) Both A and R are false.

Correct Answer: D

Solution :

For \[n=1,\,f\left( 1 \right)=\frac{1+1}{2}=1\]

For Let \[n=2,\,\,f\left( 2 \right)=\frac{2}{2}=1\]

\[\Rightarrow \,\,f\left( 1 \right)=f\left( 2 \right)=1\]

\[\Rightarrow \,\,f\left( x \right)\] is not one-one

\[\Rightarrow \] Assertion is false

{Definition of injectivity}

Also Reason [R] is true

Hence option [D] is the correct answer.