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MIT6_042JS10_lec06

# MIT6_042JS10_lec06 - Predicates Mathematics for Computer...

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1 lec 3W.1 Albert R Meyer, February 17, 2010 Predicate Logic Quantifiers , Mathematics for Computer Science MIT 6.042J/18.062J lec 3W.2 Albert R Meyer, February 17, 2010 Predicates Propositions with variables Example: [x + 2 = y] P(x,y) ::= lec 3W.3 Albert R Meyer, February 17, 2010 Predicates x = 1 and y = 3: x = 1 and y = 4: P(1,4) is false NOT (P(1,4)) is true [x + 2 = y] P(x,y) ::= P(1,3) is true lec 3W.4 Albert R Meyer, February 17, 2010 Quantifiers For ALL x There EXISTS some y x y lec 3W.5 Albert R Meyer, February 17, 2010 is like AND s . P( s ) Let s range over 6.042 staff P( s ) ::= [ s is Pumped about 6.042] same as P( Stav ) AND P( Rich ) AND P( Megumi ) AND AND P( Oscar ) lec 3W.6 Albert R Meyer, February 17, 2010 is like OR t . B( t ) Let t range over 6.042 staff B( t ) ::= [ t took 6.042 Before] same as B( Stav ) OR B( Rich ) OR B( Megumi ) OR…OR B( Oscar )

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2 lec 3W.7 Albert R Meyer, February 17, 2010 Q (y) ::= x. x < y Q (3) is T ([x<3] is T for x=1) Q (1) is T ([x<1] is T for x=0) Q (0) is F ([x<0] is not T for any x in N ) Existential Quantifier Let x, y range over N lec 3W.8 Albert R Meyer, February 17, 2010 R (y) ::= x. x < y

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