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

Options

  1. AStatement 1 is true, Statement 2 is false.
  2. BStatement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for Statement 1.
  3. CStatement 1 is false, Statement 2 is true.
  4. DStatement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1.

Correct answer

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

Step-by-step solution

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

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