For each of the following compound propositions find

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Unformatted text preview: . The operator NOR (abbreviated p q) is defined to be true iff both p and q are false. For each of the following compound propositions, find an equivalent compound proposition that uses only the NOR operator: (a) p (b) p q (c) p q 4. (a) Find a compound proposition that has the following truth table: p q r ?? T T T T T T F F T F T F T F F T F T T F F T F T F F T F F F F F (b) Explain how you could generalize your procedure to any number of variables and any truth table. This is what we mean when we say , , are a complete set of connectives. Predicates and Quantifiers 1. If P (x) is the statement "x > 0" and G(x, y) is the statement x2 y, determine the truth value of each of the following (a) P (1) (b) G(2, -3) (c) P (-1) G(-2, 1) 2. Using the same predicates as above, determine the truth values of each of the following statements if the domain is the set of all real numbers. (a) xP (x) (b) xP (x) xG(x, 0) (c) yG(2, y) 3. Suppose the domain of P (x) consists of the integers 0,1,2,3. Re-write each of the following sta...
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This note was uploaded on 02/06/2012 for the course MATHEMATIC 55 taught by Professor Robbayer during the Summer '09 term at Berkeley.

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