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Logic Leo Cheung

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Stuff you need to know Logical equivalence Write logical formula from truth table De Morgan’s Law Contrapositive If and only if Modus Ponens, Modus Tollens Quantifier

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Logically equivalence Two statement is logically equivalence if they have the same truth value in every situation

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Logically equivalence ? FFFTFF FTTFFF TFTTTT TTTFFF So they are logically equivalence

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De Morgan’s Law

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What is ? ▫ What is ? ▫ De Morgan’s Law

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Contrapositive What is the contrapositive of ▫If I do not understand the course materials, I go to tutorial. ▫Sons of Li Ka Shing are all rich. ▫

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Contrapositive Answers ▫If I don’t go to tutorial, I understand the course materials. ▫If one is not rich, he is not son of Li Ka Shing. ▫

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If and only if p if q p only if q p if and only if q Are they the same? ▫P if and only if Q ▫P = Q ▫~P if and only if ~Q They are all the same.

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Playing with if Are they the same? 1.If it rains, I will stay 2.It does not rain or I will stay 3.If I do not stay, it does not rain How about the followings? 4.If it does not rain, I do not stay 5.If I stay, it rains 6.It rains and I do not stay 1 = 2 = 3 4 = 5 ≠ 1 6 is negation of 1 1 = 2 = 3

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Modus Ponens If you know… ▫If p then q ▫p is true Conclusion: q is true

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If you skip csc2110 lecture, you will fail the course. And you really skip csc2110 lecture. Conclusion? Modus Ponens You will fail the course.

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Modus Tollens If you know… ▫If p then q ▫q is false Conclusion: p is false

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Modus Tollens If a figure is a quadrilateral, then the sum of its interior angles is 360 degree. The sum of the interior angle of a figure is not 360 degree. Conclusion? The figure is not a quadrilateral.

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Are they true? Given ▫If Leo cheats in the exam, then Leo sits in the back row. ▫Leo sits in the back row Conclusion: Leo cheats in the exam. Wrong conclusion!

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Are they true? Given ▫If interest rates are going up, stock market prices will go down. ▫Interest rates are not going up. Conclusion: Stock market prices will not go down. Wrong conclusion!

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Argument Conclusion:

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Argument Given That means must be false. Conclusion:

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Exercises Textbook ▫1.1: 31 41 47 ▫1.2: 16 38 45 ▫1.3: 3 22 41 ▫2.1: 3 9 19 ▫2.2: 3(a,c) 18 20 ▫2.3: 28 36 53 ▫2.4: 3 5 9 10 Answers can be found in the textbook.

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