EVALUATION: Prove the following. 1. Using direct proof, show that "if x and y are sum of two integer squares, then xy are also sum of two integer squares." 2. By contradiction, prove that "for all real numbers x, if x is irrational, then -x is irrational. 3. If n is an integer and n2 is divisible by 4, then n is divisible by 4. Prove or disprove by counter example.

EVALUATION: Prove the following. 1. Using direct proof, show that "if x and y are sum of two integer squares, then xy are also sum of two integer squares." 2. By contradiction, prove that "for all real numbers x, if x is irrational, then -x is irrational. 3. If n is an integer and n2 is divisible by 4, then n is divisible by 4. Prove or disprove by counter example.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.4: Mathematical Induction

Problem 46E

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