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Unformatted text preview: 1.1, 1,2 Propositions : a statement that is either true or false Exclusive OR : only one of them is T p q p q ⊕ p q p ↔ q 1 1 1 1 1 1 1 1 1 1 1 1 Implication : p → q • If p then q, p implies q, p only if q, p is a sufficient condition for q, q follows from p, q is a necessary condition for p, q if p, q when p, q whenever p, q unless ¬ p • q → p is called the converse ; ? • ¬ p → ¬ q is called the inverse ; ? • ¬ q → ¬ p is the contrapositive. ? ? Biconditional : p → q and q → p Tautology : any proposition that is always true p ∨ ¬ p Contradiction: any proposition that is always false p ∧ ¬ p Truth Table: If n propositions , then 2n rows of truth table Logical Implication : p ⇒ q If P is true Q cannot be false. • if and only if ↔ • For hiking on the trail to be safe (q), it is necessary but not sufficient that berries not be ripe along the trail (r) and for grizzly bears not to have been seen in the area (p)....
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This note was uploaded on 01/29/2012 for the course CSE 260 taught by Professor Saktipramanik during the Spring '08 term at Michigan State University.
- Spring '08