Given the functions f and sets X and Y, which of the following statements is true? f(X ∩Y ) = f(∅) = ∅, while f(A) = f(B) = {1} ⇒ f(A) ∩ f(B) = {...

Given the functions f and sets X and Y, which of the following statements is true?
f(X ∩Y ) = f(∅) = ∅, while f(A) = f(B) = {1} ⇒ f(A) ∩ f(B) = {1}.


The first statement is true, and the second statement is false.
The first statement is false, and the second statement is true.
Both statements are true.
Both statements are false.