| Assertion: The Greatest Integer Function \[f\,\,\,:\,\,\,R\to R\]given by \[f\left( x \right)=\left[ x \right]\]is not one-one. |
| Reason: A function \[f\,\,:\,\,A\to B\] is said to 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: A
Solution :
Given \[f\left( x \right)=\left[ x \right]\] Since \[\left[ 1 \right]=1,\,\,\left[ 1.1 \right]=1,\,\left[ 1.2 \right]=1\]and so on \[\therefore \]\[\left[ x \right]=a\], for \[a\le \,\,x\,\,\le \,\,a+1\,\] Given function f (x) is not one-one \[\therefore \]Assertion [A] is true Also Given Reason [R] is true and- is correct explanation of A {By definition of injective} Hence option [A] is the correct answer.
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