f2006lecNotesWeek02 - 5 5.1 Logic (cont.) Negation...

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5 Logic (cont.) 5.1 Negation verbally: not p sometimes a little messier in English: it is not the case that p symbolically: p (alternatives: ¬ p , p ) defnition using a truth table examples — based on Fipping a coin fve times state negations o±: fve heads appeared at least one head appeared both heads and tails appeared 5.2 Combining operations precedence rules be±ore , (latter two have equal precedence) can use parentheses to alter order o± evaluation examples — develop truth tables ±or expressions like p q p ( q r ) 5.3 Creating expressions for given truth tables using to write an expression with one T entry in truth table e.g. ²²T² ( p q ) using to write an expression with one ² value in truth table e.g. T²TT ( p q ) disjunctions o± conjunctions to produce truth tables with two T entries perhaps mention DN² 5.4 Conditional statements verbally: i± p then q symbolically: p q terminolgy p is the antecedant , premise ,or hypothesis q is the conclusion or consequence develop defnition with an example: p : you work hard q : you will pass this course under what conditions would we consider the statement p q to be false ? i.e. under what circunstances could you consider me a liar i± I said this? use this to build a truth table ±or p q pq p q TT T ² ²T T ²² T try to convince them that it is reasonable 11
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verbal forms for p q use an example p : I live in Toronto, q : I live in Canada to persuade them that following forms are all equivalent if p then q q if p p is sufficient for q q follows from p p only if q ??? — be careful here q is necessary for p (follows from above)
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This note was uploaded on 04/19/2008 for the course ECE 190 taught by Professor Carter during the Fall '06 term at University of Toronto- Toronto.

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f2006lecNotesWeek02 - 5 5.1 Logic (cont.) Negation...

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