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# lecture2 - Csci 2011 Lecture 2 Propositional Equivalences...

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Csci 2011: Lecture 2 Propositional Equivalences

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Last lecture Proposition Operators: NOT, AND, OR, (XOR) Conditional Statements (implication: if) Biconditional (if and only if)
not not and or xor conditional Bi- conditional p q p q p q p q p q p q p q T T F F T T F T T T F F T F T T F F F T T F F T T T F F F T T F F F T T Recap

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Exercise Verify these two equivalences using truth tables p q p q p q (p q) (q p)
Operator Precedence Not AND OR Implication Biconditional Use parentheses when in doubt

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Equivalence Some terminology regarding compound statements: Tautology: always true Example: p p Contradiction: always false Example: p p Contingency: neither a tautology or a contradiction (it depends)
Equivalence Two compound propositions p and q are logically equivalent if p q is a tautology Notation: p q We have already seen: p q p q p q (p q) (q p)

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Example p T p p T p T T T T F T F
Equivalence One way of checking for equivalence is using truth tables Lets take a closer look at implication

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lecture2 - Csci 2011 Lecture 2 Propositional Equivalences...

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