EECS 203-1: Discrete Mathematics Winter 2005 Introductory ...

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The conditional connective • One connective that gets a big workout in logic is the conditional p → q. It is read “if p then q”, ”p is sufficient for q, ”a necessary condition for p is q”, “p only if q”, and ”q whenever p”. • You can think of this as a “one-way biconditional”. The truth table is p q p → q T T T T F F F T T F F T • One way to read this table is that ”q is at least as true as p is, and maybe more,” as in the third line. Another way to read it is ”p can’t be true and q false.” This has some strange repercussions. For example, is true (by line 4). Equally, is true. if 2 + 2 = 5, then Kevin Bacon is the Pope if 2 + 2 = 5, then Kevin Bacon is not the Pope 8
Complex expressions in propositional logic • You can form “algebraic” expressions using these connectives. For example, (¬p ↔ ¬q) ↔ (¬p → (p ∨ q)) • There is a precedence scheme here, like the precedence scheme for addition, multiplication, and negation in algebraic expressions. • You can build truth tables for complex expressions. For example, consider We build the table this way: p → (¬q ∨ r). p q r ¬q (¬q ∨ r) p → (¬q ∨ r) T T T F T T T T F F F F T F T T T T T F F T T T F T T F T T F T F F F T F F T T T T F F F T T T 9
Page 1 and 2: EECS 203-1: Discrete Mathematics Wi
Page 3 and 4: Part I: Logic (Text section 1.1)
Page 5 and 6: Compound propositions • These are
Page 7: Still more operators • The exclus

EECS 203-1: Discrete Mathematics Winter 2005 Introductory ...

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