(b) Show the following. Two mappings f:X→ Y and g:X→ Y are said to be equal (and we write this f = g) if f(x) = g(x) for every x in X. Let f, g, and h be any three mappings of a non-empty set X into itself, and show that multiplication of mappings is associative in the sense that f(gh) = (fg)h.

how would you prove this

15. Let f: A → B and g: C → D. Define fx g = {(a, c), (b, d): (a, b) = f and (c,d) = g}. (a) Prove that f × g is a mapping from A × C to B x D. (b) For (a, c) = A x C, write (f× g)(a, c) in terms of f(a) and g(c).

How do you solve this question on discrete mathematics: 2. Let A be the set of all points in three-dimensional space. Define R as the relation that two points will have the same z coordinate. (a) Give three examples that are related to P(4,6,2). (b) Prove or disprove that R is reflexive. (c) Prove or disprove that R is symmetric. (d) Prove or disprove that R is transitive. (e) Is R an equivalence relation? (f) What space do all points related to each other (e.g. all points withz= 2) describe?