MAS111_09_assignment_06_hints

MAS111_09_assignment_06_hints - NANYANG TECHNOLOGICAL...

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NANYANG TECHNOLOGICAL UNIVERSITY MAS 111 FOUNDATION OF MATHEMATICS ASSIGNMENT 6 HINTS 1. Let A = { 1 , 2 } , B = { 2 , 3 , 4 , 5 } , C = { 1 , 2 , 4 , 5 , 6 , 7 } , D = { 3 , 5 , 7 , 9 } , E = { 4 , 6 , 8 } , F = { 2 , 6 } . List the elements of the following sets: B C , B C , C - E , B 4 E , A B , A C , A ( B C ), ( C - B ) - A , ( C - A ) - B , P ( F ), ( A E ) - ( C E ), P ( E ) - P ( C ), ( B - A ) F . Hint : These are exercises for the understanding of basic set operations. 2. Let A,B,C be any sets. Prove that ( A B ) C = ( A C ) ( B C ). Proof : Let x be any element. Then x ( A B ) C x A B and x C ( x A or x B ) and x C ( x A and x C ) or ( x B and x C ) x A C or x B C x ( A C ) ( B C ) Therefore, ( A B ) C = ( A C ) ( B C ). 2 3. Let A,B,C be any sets. Prove that
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(a) ( A - B ) - C = ( A - C ) - B . (b) ((
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MAS111_09_assignment_06_hints - NANYANG TECHNOLOGICAL...

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