Assume that f:A-->B and X,Y are subsets of A.

Prove: If f is one-to-one and f(X) is a subset of f(Y), then X is a subset of Y.

Anything helps :) Thank you!

f : A → B
X, Y ⊆ A
f is 1-1 and f(X) ⊆ f(Y)

Prove X ⊆ Y

Let x ∈ X. Let b = f(x). Then b ∈ f(X). Since f(X) ⊆ f(Y), then

b ∈ f(Y). So b = f(y) for some y ∈ Y. Since f is one-to-one

and f(x) = b = f(y), then x = y. So x ∈ Y. Hence if x ∈ X,

then x ∈ Y. This means that X ⊆ Y.