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Unformatted text preview: UNIT: SIT192 Discrete Mathematics 2010 Trimester 3 1 Attempt all questions . 1. (a) The propositions p , q , r , and s are defined by: p : Vicky bakes muffins q : Vicky bakes scones r : Vicky bakes sour dough s : Vicky bakes raisin bread Express the following in symbolic form: (i) Vicky bakes muffins, but she bakes neither raisin bread nor sour dough. (ii) Vicky doesnt bake raisin bread, if she bakes either scones or sour dough. (iii) Vicky bakes muffins if and only if she bakes scones and sour dough. (iv) If Vicky bakes neither scones nor raisin bread, she bakes muffins. (b) Construct the truth table for p ( q r ). (c) (i) Use the truth tables to prove p q p q . (ii) Use the result obtained in Part (i), and the laws of logical equivalence to prove q ( p q ) q p . (d) Given that the universe of discourse is all the integers , determine the truth values of the following statements: (i) x y : ( x + y ) 2 = x 2 + 3 x + y 2 . (ii) y x : ( x y ) 2 = 2 x 2 + y 2 . Note: in each case, provide a reason for the answer. [6+5+7+4=22 marks] UNIT: SIT192 Discrete Mathematics 2010 Trimester 3 2 2. The universal set U is given by U = { x N : 25 x 50 } , where N = { 1 , 2 ,...
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This note was uploaded on 10/03/2011 for the course SIT 192 taught by Professor Nothing during the Three '11 term at Deakin.
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