# lecture05 - MA1100 Lecture 5 Logic Converse and...

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1 MA1100 Lecture 5 Logic Converse and Contrapositive Biconditionals Tautologies and Contradictions Logical Equivalence Chartrand: section 2.6 – 2.9

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Lecture 5 2 Summary (from last lecture) Symbolic form Disjunction Conjunction Implication Negation When is it false? Standard form Operator P and Q P or Q not P If P then Q P Q P ¤ Q ~ P P Q Other forms of implication ( necessary, sufficient, only if )
Lecture 5 3 Implication If 2 is on one side of the card, then A is on the other side Example If A is on one side of the card, then 2 is on the other side

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Lecture 5 4 Converse Q P is called the converse of P Q T T F T P Q T F F F F T T T Q P Q P An implication does not have the same meaning as its converse . Truth table of P Q vs Q P
Lecture 5 5 T T F T P Q F T F T F F T F T T T T Q P Q P Converse If x is odd, then x is a prime If x is a prime, then x is odd Example Truth table of P Q vs Q P converse P Q and Q P cannot be false at the same time.

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Lecture 5 6 Biconditional statement Symbolic form: P Q Standard form: P if and only if Q Example Truth Table F T F T F F F F T T T T P Q Q P x is even if and only if x 2 is even P Q is true when P and Q have exactly the same truth value
Lecture 5 7 Biconditional statement Standard form: P if and only if Q Truth Table T T F T P Q T F T T Q P T F F F F T T T P Q Q P T F F T P Q is true provided both P Q and Q P are true Meaning: ( If P then Q) and ( If Q then P) P Q is the same as (P Q) (Q P)

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Lecture 5 8 Biconditional statement Standard form: P if and only if Q Examples x being even is necessary and sufficient for x 2 to be even Other forms: P is necessary and sufficient for Q P and Q are equivalent x is even if and only if x 2 is even x being even is equivalent to x 2 being even
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## This note was uploaded on 04/15/2010 for the course MATHS MA1101R taught by Professor Vt during the Spring '10 term at National University of Singapore.

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lecture05 - MA1100 Lecture 5 Logic Converse and...

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