I'm self-learning RA and I've got a question
Assume that I have proved that for a function g: R -> R is always true that g(A ∩ B) ⊆ g(A) ∩ g(B) for all sets A, B ⊆ R.
Can I also prove that g(A ∩ B) ⊇ g(A) ∩ g(B)? If so, where should I start? ( I'm a complete noob at proofs yet)
Thanks!
Assume that I have proved that for a function g: R -> R is always true that g(A ∩ B) ⊆ g(A) ∩ g(B) for all sets A, B ⊆ R.
Can I also prove that g(A ∩ B) ⊇ g(A) ∩ g(B)? If so, where should I start? ( I'm a complete noob at proofs yet)
Thanks!