Suppose you have to use an element argument toprove the following statement. (Assume that all setsare subsets of a universal set U.)For all sets A, B, and C(A – B) n (C - B) C (AnC)- B.Consider the sentences in the following scrambled list.• Therefore a E (AnC) - B by the definition ofset difference.• We must show that E (AnC)- B.• Thus x € AnC by definition of intersection,and, in addition, x ¢ B.• Thus, by definition of intersection, x € A andx€ C, and, in addition, a4 B.• By definition of intersection,те (А — В)П (С — B).• By definition of intersection, r E A - B andTE C - B.Suppose A, B, and C are any sets andx E (AnC) – B.• We must show that a E (A B) n(C- B).• Suppose A, B, and C are any sets andхе (А- В)n(С - В).• By definition of set difference, E A-B andx € C - B.• By definition of set difference, r E A and a Band a € C and a ¢ B.• By definition of intersection, a € A and a Band æ e C and e ¢ B.

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Description: Suppose you have to use an element argument toprove the following statement. (Assume that all setsare subsets of a universal set U.)For all sets A, B, and C(A – B) n (C - B) C (AnC)- B.Consider the sentences in the following scrambled list.• Therefo

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Suppose you have to use an element argument to prove the following statement. (Assume that all sets are subsets of a universal set U.) For all sets A, B, and C (A – B) n (C - B) C (AnC)- B. Consider the sentences in the following scrambled list. • Therefore a E (AnC)- B by the definition of set difference. • We must show that E (AnC)- B. • Thus x € An C by definition of intersection, and, in addition, a ¢ B. Thus, by definition of intersection, x € A and x E C, and, in addition, x B. By definition of intersection, те (А - В)П (С — B). • By definition of intersection, E A - B and x E C - B. Suppose A, B, and C are any sets and x E (AnC) - B. We must show that a E (A - B) n (C - B). Suppose A, B, and C are any sets and те (А - В)n(С - В). • By definition of set difference, r E A - B and x € C - B. • By definition of set difference, r E A and a ¢ B and a e C and a ¢ B. • By definition of intersection, r E A and a B and æ € C and e¢B.

Suppose you have to use an element argument to prove the following statement. (Assume that all sets are subsets of a universal set U.) For all sets A, B, and C (A – B) n (C - B) C (AnC)- B. Consider the sentences in the following scrambled list. • Therefore a E (AnC)- B by the definition of set difference. • We must show that E (AnC)- B. • Thus x € An C by definition of intersection, and, in addition, a ¢ B. Thus, by definition of intersection, x € A and x E C, and, in addition, x B. By definition of intersection, те (А - В)П (С — B). • By definition of intersection, E A - B and x E C - B. Suppose A, B, and C are any sets and x E (AnC) - B. We must show that a E (A - B) n (C - B). Suppose A, B, and C are any sets and те (А - В)n(С - В). • By definition of set difference, r E A - B and x € C - B. • By definition of set difference, r E A and a ¢ B and a e C and a ¢ B. • By definition of intersection, r E A and a B and æ € C and e¢B.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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