Question

Let A and B be non empty sets in R and f : $A\to B$ is a bijective function.
Statement 1 : f is an onto function.
Statement 2 : There exists a function g : $B\to A$ 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.
• D. Statement 1 is true, Statement 2 is true. Statement 2 is not the correct explanation for Statement 1.

Answer 1

Answer: (D)

Let A and B be non-empty sets in R.
Let f : $A\to B$ 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