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Unformatted text preview: Administration Midterm 1 is not early after all. We dont think 3 weeks is enough material to merit a midterm. CS70: Lecture 3. Outline. 1. Proofs 2. Simple 3. Direct 4. by Contrapositive 5. by Cases 6. by Contradiction Simple theorem.. Theorem: P = ( P Q ). Proof: I P is true. Simple theorem.. Theorem: P = ( P Q ). Proof: I P is true. P Q is true Simple theorem.. Theorem: P = ( P Q ). Proof: I P is true. P Q is true anything = true is true Simple theorem.. Theorem: P = ( P Q ). Proof: I P is true. P Q is true anything = true is true so X = ( P Q ) is true for all X , Simple theorem.. Theorem: P = ( P Q ). Proof: I P is true. P Q is true anything = true is true so X = ( P Q ) is true for all X , and in particular, P = ( P Q ) is true Simple theorem.. Theorem: P = ( P Q ). Proof: I P is true. P Q is true anything = true is true so X = ( P Q ) is true for all X , and in particular, P = ( P Q ) is true I P is false. Simple theorem.. Theorem: P = ( P Q ). Proof: I P is true. P Q is true anything = true is true so X = ( P Q ) is true for all X , and in particular, P = ( P Q ) is true I P is false. false = anything , is true Simple theorem.. Theorem: P = ( P Q ). Proof: I P is true. P Q is true anything = true is true so X = ( P Q ) is true for all X , and in particular, P = ( P Q ) is true I P is false. false = anything , is true so P = anything is true . Simple theorem.. Theorem: P = ( P Q ). Proof: I P is true. P Q is true anything = true is true so X = ( P Q ) is true for all X , and in particular, P = ( P Q ) is true I P is false. false = anything , is true so P = anything is true . in particular P = ( P Q ) is true . Simple theorem.. Theorem: P = ( P Q ). Proof: I P is true. P Q is true anything = true is true so X = ( P Q ) is true for all X , and in particular, P = ( P Q ) is true I P is false. false = anything , is true so P = anything is true . in particular P = ( P Q ) is true . More detailed but the same as truth table proof in some sense. Proof by truth table. Theorem: P = ( P Q ). Proof by truth table. Theorem: P = ( P Q ). Proof: P Q P Q T T T T F T F T T F F F Proof by truth table. Theorem: P = ( P Q ). Proof: P Q P Q T T T T F T F T T F F F Look only at appropriate rows. Where theorem condition is true. Proof by truth table....
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This note was uploaded on 02/29/2012 for the course COMPSCI 70 taught by Professor Rau during the Fall '11 term at University of California, Berkeley.
 Fall '11
 Rau

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