hw04 - Exercise 11. Let a,b,c Z . Prove that if a divides...

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Intro to Abstract Math Homework 4 Fall 2009 Due September 11 Exercise 10. Let P , Q and R be statements. Verify the following logical equivalences. a. P ( Q R ) = ( P Q ) ( P R ) b. ( ¬ P ) ( R ( ¬ R )) = P c. ¬ ( P Q ) = P ( ¬ Q ) d. P ( Q R ) = ( P Q ) ( P R ) e. P Q = ( P Q ) (( ¬ P ) ( ¬ Q )) Definition: Let m,n Z . We say that m divides n if there is a k Z so that n = km .
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Unformatted text preview: Exercise 11. Let a,b,c Z . Prove that if a divides both b and c then a divides b + c . Exercise 12. Let a,b,c Z . Prove that if a divides both b and c then a divides bc . Can you modify your proof to yield a slightly stronger statement?...
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