Let A and B be non empty sets in R and f : A ® B is a biective function. Statement 1: f is an onto function. Statement 2: There exists a function g : B ® A such that fog = IB .

Question:

Let $A$ and $B$ be non empty sets in $R$ and $f: A \rightarrow B$ is a bijective function.

Statement 1: f is an onto function.

Statement 2: There exists a function $g: B \rightarrow A$ such that fog $=I_{B}$.

  1. Statement 1 is true, Statement 2 is false.

  2. Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for Statement 1 .

  3. Statement 1 is false, Statement 2 is true.

  4. Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1 .


Correct Option: 4

JEE Main Previous Year 1 Question of JEE Main from Mathematics Sets, Relations and Functions chapter.
JEE Main Previous Year Online May 26, 2012

Solution:

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