Lecture2a.pdf - Lecture 2a Today I §6 Counterexamples I Disprove statements that are false by providing a counterexample I §7 Boolean Algebra I Define

# Lecture2a.pdf - Lecture 2a Today I §6 Counterexamples I...

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Lecture 2a Today: I § 6: Counterexamples I Disprove statements that are false by providing a counterexample I § 7: Boolean Algebra I Define Boolean algebra and its basic operations I Show two statements are logically equivalent I Determine if Boolean expressions are tautologies, contingencies or contradictions Homework: I Read § 8-9. I HW1 due Fri, Feb 8.

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(Dis)proof by Counterexamples Prove or disprove: 1. Porcupines are mammals. 2. Mammals are porcupines. TRI Let x be a porcupine Then it gives birth to live young , it is warm blooded , and it feeds its young with milk Therefore , X is a mammal FALSE Berg are mammals that are not porcupines It Counterexample -
Counterexamples for If-Then Statements To show A = ) B is false: I Find an instance where A is true, but B is false. I Just one counterexample disproves a statement! Note: Proof by example is NOT valid. u 71 - - - - [ We need to prove statements in general Examples does not suffice , because they are too specific

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Counterexamples for If and Only If Statements To show A () B is false: I Find an instance where A is true, but B is false. OR I Find an instance where B is true, but A is false. y I my " A B " AND "B⇒A " - - Prove " A B " false ÷ Prove " B A " false
Exercises

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Definition (Divisible) An integer a is divisible by integer b , denoted b | a , provided there exists an integer c such that a = bc .
• Fall '11
• Elsey
• Logic, Basic Operations

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