Adv Alegbra HW Solutions 39

Adv Alegbra HW - 39 2.2 If A and B are subsets of a set X prove that A B = A B where B = X B is the complement of B Solution This is one of the

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39 2.2 If A and B are subsets of a set X , prove that A B = A B 0 , where B 0 = X B is the complement of B . Solution. This is one of the beginning set theory exercises that is so easy it is dif f cult; the dif f culty is that the whole proof turns on the meaning of the words and and not. For example, let us prove that A B A B 0 . If x A B , then x A and x / B ; hence, x A and x B 0 , and so x A B 0 . The proof is completed by proving the reverse inclusion. 2.3 Let A and B be subsets of a set X . Prove the de Morgan laws ( A B ) 0 = A 0 B 0 and ( A B ) 0 = A 0 B 0 , where A 0 = X A denotes the complement of A . Solution. Absent. 2.4 If A and B are subsets of a set X ,de f ne their symmetric difference (see Figure 2.5) by
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This note was uploaded on 12/21/2011 for the course MAS 4301 taught by Professor Keithcornell during the Fall '11 term at UNF.

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