Suppose and are two sets and is a function. For a subset of ,define to be the subset { } of .For a subset of ,define to be the subset { : } of .Then which of the following statements is true?

(A) for every

(B) for every if and only if

(C) for every

(D) for every if and only if

To me it appears that every option is correct.But then I think conditions for inverse are also to be applied .

Please explain as to why (A),(B),(C) are wrong and why (D) is correct.I am not being able to put concepts of ONE-ONE and ONTO functions in place