9 - The University of Sydney MATH 1004 Second Semester...

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The University of Sydney MATH 1004 Second Semester Discrete Mathematics 2011 Tutorial 9 Week 10 1. Draw truth tables for the following propositions. ( i ) ( p q ). ( ii ) p ∧ ∼ q . ( iii ) p ( p q ). 2. Show that the following pairs of propositions are equivalent: ( i ) ( p q ) r ; ( p ∧ ∼ q ) r . ( ii ) p ⇒ ∼ q ; q ⇒ ∼ p . 3. Decide whether the following propositions are true or false: ( i ) If 1 + 1 = 2, then 2 + 2 = 5. ( ii ) If 1 + 1 n = 2, then pigs might Fy. ( iii ) If 1 + 1 = 2, then 2 + 3 = 5. 4. Show that ( p q ) ( p q ) p is a tautology. 5. Show that ( p q ) ∧ ∼ ( p q ) is a contradiction. 6. Taking the universal set to be the set R of all real numbers, determine the truth or falsity of the following sentences. ( i ) ( x ) ( ( x Z ) ( x 2 x 1 > 0) ) . ( ii ) ( x ) ( ( x Z ) ( x 2 x 1 > 0) ) .

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This note was uploaded on 09/01/2011 for the course YEAR 1 taught by Professor Various during the Three '11 term at University of Sydney.

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9 - The University of Sydney MATH 1004 Second Semester...

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