I’m working on a set theory question and need support to help me learn.Problem
1:Let A, B be sets and let f:A→B. f is surjective if and only if for all Y⊆ B,Y ⊆ f(f^−1(Y)).Problem
2:Let G be a group, let H be a subgroup of G, and let a ∈ G. Let f:H→aH given by f(h) =ah^−1 for all h ∈ H and let g: aH→H given by g(x) =x^− a for all x ∈ aH .[Note that in the definition of g above, it’s not obvious that g is actually a function; that is, it’snot obvious that g(x)∈H.]Prove that g(x)∈Hf or all x∈a Hand prove that g is the inverse off.
Requirements: 200
