Unformatted text preview: m 2 = n 2 , so we conclude this direction is true. ∴ m 2 = n 2 ⇔ m = n or m =n 3. (4 pts) Prove that if x + y is irrational, then either x is irrational or y is irrational. We’ll do this by contrapositive. That is, we’ll show that x ∈ Q and y ∈ Q ⇒ x + y ∈ Q Suppose x,y ∈ Q and let a,b,c,d ∈ Z such that x = a b ,y = c d . Then x + y = a b + c d = ad + cb bd ∈ Q (since ad + cb,bd ∈ Z ) Thus, we have the desired result....
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 Summer '08
 STRAIN
 Math, Logic, AD + CB, Rob Bayer, true. m2

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