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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. Well do this by contrapositive. That is, well 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