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4. Let P denote the following sentence: Let n, d, p E Z be integers such that d> 0 and p is prime. If d divides n and 1 or p divides n. d divides n + p, then d = (a) Write P as a logical sentence using quantifiers (V, 3) and logical connectives (^, V, ⇒, etc.). (b) Write the negation P. (c) Which statement is true, P or -P? Prove the true statement.

4. Let P denote the following sentence: Let n, d, p E Z be integers such that d> 0 and p is prime. If d divides n and 1 or p divides n. d divides n + p, then d = (a) Write P as a logical sentence using quantifiers (V, 3) and logical connectives (^, V, ⇒, etc.). (b) Write the negation P. (c) Which statement is true, P or -P? Prove the true statement.

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter4: Polynomials
Section4.1: Exponents
Problem 24OE
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4. Let P denote the following sentence: Let n, d, p = Z be integers such that d> 0 and p is prime. If d divides n and = 1 or p divides η. d divides n + p, then d (a) Write P as a logical sentence using quantifiers (V, 3) and logical connectives (^, V, ⇒, etc.). (b) Write the negation P. (c) Which statement is true, P or ¬P? Prove the true statement.
Transcribed Image Text:4. Let P denote the following sentence: Let n, d, p = Z be integers such that d> 0 and p is prime. If d divides n and = 1 or p divides η. d divides n + p, then d (a) Write P as a logical sentence using quantifiers (V, 3) and logical connectives (^, V, ⇒, etc.). (b) Write the negation P. (c) Which statement is true, P or ¬P? Prove the true statement.
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