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Unformatted text preview: AT AF Nei q + x is irrational. AT AF Nei Essay questions. Please write in complete sentences. C3: Prove that 15 is irrational. Now prove that 3 + 5 is irrational. C4: Consider two posints A and B . Prove directly, using WO, that there is a posint D st. D Z = A Z + B Z . [ Hint: Dont forget to rst show that A Z + B Z has a nonzero element.] C5: Prove that there are innitely many prime numbers. End of ExamC C1: 70pts C2: 40pts C3: 80pts C4: 80pts C5: 80pts Total: 350pts Print name ............................................. Ord: Honor Code: I have neither requested nor received help on this exam other than from my professor (or his colleague) . Signature: ............................................
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 Summer '08
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