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05 Slides--Equivalences

# 05 Slides--Equivalences - CS103 HO#5 Equivalences Homework...

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CS103 HO#5 Equivalences March 31, 2010 1 9 written problem sets, counted equally Due in class 3 free late days (max. 1 on any assignment) Not accepted more than one class period late! Late without a late day: -10% You may work with others in the class, but you must write up your problem sets individually Revealing an answer denies the other person the opportunity for the "Aha!" experience Homework Policy pq ? T T T F F T F F How many binary logical operators can there be? p q p ? q T T T T F F F T T F F T p q p ? q T T T T F F F T T F F T Observation 1: The ? connective is pretty weak. Knowing that p ? q is true only eliminates one possible combination of p and q . Observation 2: If we know p ? q is true and we also know p is false, then we have no information about the truth of q . Observation 3: If we know p ? q is true and we also know p is true, then we are sure q is true. The Conditional operator p q p q ¬ p q T T T T T F F F F T T T F F T T p q ¬ p q p q p q ¬ p q T T T T T F F F F T T T F F T T is called the material conditional , meaning that it is truth-functional The Conditional operator

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CS103 HO#5 Equivalences March 31, 2010 2 p q p q ¬ p q T T T T T F F F F T T T F F T T The best rendering of
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05 Slides--Equivalences - CS103 HO#5 Equivalences Homework...

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