Suppose f: X --- Y. A subset Y and B subset Y. Prove that if A is a subset of B then f^-1(A) is a subset of f^-1(B).

Question

Suppose f: X ---> Y. A subset Y and B subset Y. Prove that if A is a subset of B then f^-1(A) is a subset of f^-1(B).

anonymous · Answer

Suppose Y = {a,b,c} and A = {a} and B = {a,b} and X = { 1,2,3}
f:X-->Y = { (1,a), (2,b), (3,c) }
f^-1(A) = f^-1(a) = 1
f^-1(B) = {f^-1(a), f^-1(b)} = {1,2}
Clearly, f^-1(A) is a subset of f^-1(B)

swissgirl · Answer

Not sure if you can prove like that

swissgirl · Answer

You must prove using general statements

anonymous · Answer

How would you solve it @swissgirl?

anonymous · Answer

Those are general statements if you substitute 1,2,3 with some variables like p,q,r

anonymous · Answer

The preimages of the elements of A will be also included in the preimages of the elements of B, as A is a subset of B

anonymous · Answer

@AbhimanyuPudi, you have taken a specific case, you need a general proof