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. |
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