Q44 / 90 · JEE Main 2012 (26 May Online) · Mathematics

Let $A$ and $B$ be non empty sets in $R$ and $f: A \rightarrow B$ is a bijective function. Statement 1: $\mathrm{f}$ is an onto function. Statement 2: There exists a function $g: B \rightarrow A$ such that fog $=I_B$.

  • A
    Statement 1 is true, Statement 2 is false.
  • B
    Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for Statement 1.
  • C
    Statement 1 is false, Statement 2 is true.
  • Correct answer
    D
    Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1.

Solution

Let $A$ and $B$ be non-empty sets in $R$. Let $f: A \rightarrow B$ is bijective function. Clearly statement - 1 is true which says that $f$ is an onto function. Statement $-2$ is also true statement but it is not the correct explanation for statement-1

Hence, the correct answer is option: 'D'.

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