Part 2: Proof that (A n C) – BC (A – B)n (C – B) Consider the sentences in the following scrambled list. By definition of intersection, x E (A – B) n (C – B). By definition of set difference x E An C...

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Extracted text: Part 2: Proof that (A n C) – BC (A – B)n (C – B) Consider the sentences in the following scrambled list. By definition of intersection, x E (A – B) n (C – B). By definition of set difference x E An C and x ¢ B. By definition of intersection, x E A and x E C. By definition of set difference, x E A and x C. So by definition of set difference, x E A – B and x E C – B. By definition of intersection xE An C and x ¢ B. Hence both xE A and x € B and also x E C, and x & B. We prove part 2 by selecting appropriate sentences from the list and putting them in the correct order. 1. Suppose x E (A n C) – B. 2. By definition of intersection, x e (A – B) n (C – B). - 3. So by definition of set difference, x e A - B and x e C - B. 4. ---Select--- 5. ---Select--- 6. Hence both x e A and x ¢ B and also x e C, and x ¢ B. 7. Hence, (A n C) – BC (A – B) n (C – B) C by definition of subset.