let f: A → B and let W, X ⊆ A.
Prove that if W ⊆ X, then g(W) ⊆ f(X)
I don't see how this can work, as I think I've found a counter example. Yet the instructions ask for a proof.
Let A = {0,1,2}
Let X = {0,1}
Let W = {0}
Then let f(x) = x+1 & let g(w) = w
Then g(0) = 0
f(0) = 1
f(1) = 2
So this satisfies all conditions, doesn't it? Yet, g(W) isn't a subset of f(X). Where have I gone wrong?