If f : X -> Y and a, b ⊆ X, then f (a ∩ b) is equal to ans. f(a) - f(b) f(a) ∩ f(b) a proper subset of f(a) ∩ f(b) f(b) - f(a)

The correct answer is f(a) ∩ f(b).

Here's why:

Given two subsets a and b of X, the intersection of a and b (a ∩ b) is the set of elements that are common to both a and b.

When we apply the function f to this intersection, we get the set of images of the elements that are common to a and b. This is the same as the intersection of the images of a and b under f, which is f(a) ∩ f(b).

So, f(a ∩ b) = f(a) ∩ f(b).

The other options are not generally true. For example, f(a) - f(b) would be the set of images of elements in a that are not in b, which is not necessarily the same as the image of the intersection of a and b. Similarly, f(a ∩ b) is not necessarily a proper subset of f(a) ∩ f(b), and f(b) - f(a) is not necessarily the same as the image of the intersection of a and b.