Bridge to Abstract Mathematics: Mathematical Proof and Structures

292 RELATIONS: FUNCTIONS AND MAPPINGS Chapter 8

2. Suppose at = (A$ E I) is a collection of sets and J c I. Prove:


3. Suppose at = (A$ E I) is a pairwise disjoint collection of sets; that is, for any
   A, ~EI with I # p, we have A, n A, = (a. Prove that n,,, A, = (a.


4. Let f: X -r Y be a mapping. Let d = {A, 1 A E I) and 461 = {B, I p E J) be collec-
   tions of subsets of X and Y, respectively. Prove:


5. Let d = {A,(A E I) be a collection of subsets of a set X. Suppose the indexing
   set I is empty. Prove, in this case, that: