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MATH135_W12_Assignment_1_Solns

MATH135_W12_Assignment_1_Solns - 1 MATH 135 W 2012...

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1 MATH 135 W 2012: Assignment 1 Due: 8:30 AM, Wed., 2012 Jan. 25 in the dropboxes outside MC 4066 Write your answers in the space provided. If you wish to typeset your solutions, use the solution template posted on the course web site. Typesetting is done in L A T E X. A very good online all purpose L A T E Xmanual is the L A T E Xwikibook at http://en.wikibooks.org/wiki/LaTeX . Links to installations for various operating systems are also included there. Stephen Carr is IST’s L A T E Xgoto person, and his introductory guide is at http://www.ist.uwaterloo.ca/ew/saw/latex/latex_getstarted.pdf . Family Name: Solutions First Name: I.D. Number: Section: Mark: (For the marker only.) If you used any references beyond the course text and lectures (such as other texts, discussions with colleagues or online resources), indicate this information in the space below. If you did not use any aids, state this in the space provided. 1. Use a truth table to determine whether or not ¬ ( A B ) A ( ¬ B ). A B A B ¬ ( A B ) ¬ B A ( ¬ B ) T T T F F F T F F T T T F T T F F F F F T F T F Because the columns for ¬ ( A B ) and A ( ¬ B ) are the same, the two statements are logically equivalent.
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2 2. Use a truth table to determine whether or not A ( B C ) is equivalent to ( A B ) ( A C ). A B C B C A ( B C ) A B A C ( A B ) ( A C ) T T T T T T T T T T F T T T F T T F T T T F T T T F F F F F F F F T T T F F F F F T F T F F F F F F T T F F F F F F F F F F F F Because the columns for A ( B C ) and ( A B ) ( A C ) are the same, the two statements are logically equivalent. 3. This question deals with sets. (a) Give a specific example to show that the statement “ U ( S T ) = ( U S ) T ” is false. Let U = , S = { 1 } and T = { 2 } . Then U ( S T ) = and ( U S ) T = { 2 } . In this case U ( S T ) 6 = ( U S ) T (b) Prove the following proposition.
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