Problems 1.1 1. Given any functions f: A→ k: B, B2, show that → A1, g: B→ B1, h: A, A2 and (h x k) o (f x g) *(8 o 4) x (fo 4) 2. Given functions f: A A and g: В B, show that - po (f x g) = f op A x B...

Extracted text: Problems 1.1 1. Given any functions f: A→ k: B, B2, show that → A1, g: B→ B1, h: A, A2 and (h x k) o (f x g) *(8 o 4) x (fo 4) 2. Given functions f: A A and g: В B, show that - po (f x g) = f op A x B A is the projection function. 3. If f: A bijection and that (g of)-1 = f-1og-1. 4. If f: A → B and g: C→ D are injections, show that f x g is an injection and that (f x g)-1 = f-1 x g-1. 5. Given any functions f: A B, g: A C, h: B-→ B1, k: B→ B2 and q: C C,, show that where p: B and g: B-C are bijections, show that gof is a %3D (i) (h, k) o f = (h o f, ko f) (ii) (h x q) • (f, g) = (h f, q ° g).