exer1-11

# exer1-11 - MACM 101 Discrete Mathematics I Exercises on...

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MACM 101 — Discrete Mathematics I Exercises on Propositional Logic. Due: Friday, Septem- ber 30th (at the beginning of the class) Reminder: the work you submit must be your own. Any collaboration and consulting outside resources must be explicitly mentioned on your submission. Please, write with a pen, not a pencil. 30 points will be taken oﬀ the mark of works written in pencil. 1. Construct a truth table for the following compound statement: ( p q ) ( q ⊕¬ r ). 2. Determine whether the following compound statement is a tautology ( ¬ p ( p q )) → ¬ q. 3. Show that ( p r ) ( q r ) and ( p q ) r are logically equivalent. 4. Show that ( p q ) r and ( p r ) ( q r ) are not logically equivalent. Do not use truth tables. 5. Simplify the compound statement ¬ ( p ( q r ) (( p q ) r )) . 6. Prove that the Rule of Syllogism is a valid argument. 7. Each of two rooms (room I and room II) contains either a lady or a tiger. If a room

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## This note was uploaded on 09/25/2011 for the course CHEM 281 taught by Professor Williams during the Spring '11 term at Simon Fraser.

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exer1-11 - MACM 101 Discrete Mathematics I Exercises on...

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