22_proofsII

22_proofsII - Introduction to Computers and Programming...

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Introduction to Computers and Programming Prof. I. K. Lundqvist Lecture 22 May 11 2004 Elementary Logic either true or false, not both propositions ¬ “and” “or” “if and only if” “implies” “is true if for all x in U, p(x) is true” Proposition is sentence that can be Symbolic notations for manipulating logic of “not” or negation •Quan t i f
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Elementary Logic Æ p is called the converse of p Æ q, and ¬ q Æ ¬ p is the contrapositive of p Æ q Example: propositions •q Æ r 2 = x, then x = 0 or x = 1 above propositions Example : go shopping. P: I go to Harry’s Q: I go to the country R: I will go shopping If. ..... P...... or. ....Q. ....then. ...not. ....R (P Q) R • The proposition q – Give the converse of the following • If I am smart, then I am rich •I fx • If 2 + 2 = 4, then 2 + 4 = 8 – Give the contrapositives for the propositions Breaking assertions into component - look for the logical operators!
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Elementary Logic p, q, r and logical connectives are clouds in the sky Convert the following into predicate logic sentences can can do a trick Let p, q, r be the following propositions p = “it is raining” q = “the sun is shining” r = “there are clouds in the sky” Translate the following into logical notation, using
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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.

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22_proofsII - Introduction to Computers and Programming...

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