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Unformatted text preview: Math 135: Lecture 10: Negations Exercise 10.1. Negate each of the following statements. Whenever possible, avoid the use of the English words “no” or “not”. 1. d | a and d | b . 2. There are an infinite number of primes. 3. (Goldbach’s Conjecture) Every even integer greater than two can be written as the sum of two primes. Original : If A , then B Converse : If B , then A Contrapositive : If ¬ B , then ¬ A Inverse : If ¬ A , then ¬ B Exercise 10.2. For each of the following statements, write the converse, contrapositive and inverse. Whenever possible, avoid the use of the English words “no” or “not”. 1. If x ≥ 2, then x 2- 4 ≥ 0. Converse: Contrapositive: Inverse: 2. If p is a prime and p | ab , then p | a or p | b . Converse: Contrapositive: Inverse: Negating Statements with Quantifiers • The negation of a universal statement results in an existential statement....
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This note was uploaded on 10/27/2011 for the course MATH 135 taught by Professor Andrewchilds during the Fall '08 term at Waterloo.
- Fall '08