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- Use a proof by contraposition to show that If m2 + n2 is an odd integer, then m is odd or n is odd.
- Let p be “if m2 + n2 is an odd integer” and q be “m is odd or n is odd”.
- Contrapositive is “If neither m is odd nor n is odd, then m2 + n2 is not odd”
- Which is the same as “If m and n are even, m2 + n2 is even”
- m2 + n2 = 2km2 + 2kn2 definition of an even number
- = 2(km2 + kn2) Factor out a 2
- = 2(k’) k’ = km2 + kn2
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