# am_lect_04 - Announcements HW 1 released last Friday due...

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Announcements HW 1 released last Friday, due this Friday http://www.cs.uiuc.edu/class/sp10/cs173

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Logical Equivalences Definition: Two propositions p and q are logically equivalent if they have the same truth-tables (notation: p q ) Examples : ( p q ) ( ¬ p q ) ¬ ( p q ) ( ¬ p ) ( ¬ q ) ¬ ( p q ) ( ¬ p ) ( ¬ q ) Try one: Show that p ( q r ) is logically equivalent to ( p q ) ( p r ) p q r p ( q r ) ( p q ) ( p r ) T T T T T T T F T T T F T T T T F F T T F T T T T F T F F F F F T F F F F F F F
Negating Propositions DeMorgan’s Laws and the fact that ¬ ( ¬ ( p )) p are useful Another useful fact: ¬ ( p q ) ≡ ¬ ( ¬ p q ) by the earlier equivalence ( ¬ ( ¬ p )) ( ¬ q ) by DeMorgan’s Law p ( ¬ q ) Example : Negate: “If it rains then the road gets slippery” — “if p then q is the same as p q — It rains and the road does not get slippery

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## This note was uploaded on 12/24/2010 for the course CS CS 173 taught by Professor Fleck during the Spring '10 term at University of Illinois, Urbana Champaign.

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am_lect_04 - Announcements HW 1 released last Friday due...

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