Week 7 Tutorial - a A-B-C = A-C-B b A ∪ C = B ∪ C = ⇒...

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Concordia University COMP 232/2 Mathematics for Computer Science FALL 2010 Tutorial Problems (Section DD) : Week 7 7-1. Show that if A B then P ( A ) P ( B ). 7-2. Let the predicates P , Q , R , and S be defined as P ( x ) : x 3 1 , Q ( x ) : x 2 = 2 , R ( x ) : x < x 2 , S ( x ) : - 5 x +5 , with the domain of x being the set of integers. Enumerate the truth set of each of the three predicates below. a) P ( x ) S ( x ) b) Q ( x ) S ( x ) c) R ( x ) S ( x ) 7-3. Let A , B , and C be sets. For each of the following statements, if true then give a proof and if false then give a counterexample.
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Unformatted text preview: a) ( A-B )-C = ( A-C )-B b) A ∪ C = B ∪ C = ⇒ A = B c) A ∩ C = B ∩ C = ⇒ A = B d) [ A ∪ C = B ∪ C ] ∧ [ A ∩ C = B ∩ C ] ⇐⇒ A = B 7-4. Find S ∞ i =1 A i and T ∞ i =1 A i for each of the following. a) A i = { i, i + 1 , i + 2 , ... } b) A i = { , i } c) A i = { x ∈ R | < x < i } d) A i = { x ∈ R | x > i } 17-Oct-2010, 10:50 am...
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This note was uploaded on 11/15/2010 for the course ENCS COMP 232 taught by Professor Ford during the Fall '10 term at Concordia University Irvine.

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