Question

3.51. Let x ? Z. Use one or two lemmas to prove that 3.52. Give a direct proof of the following: Let x ? Z. If 11x – 5 is odd, then x is even. 3.53. Let x, y ? Z. Prove that if x + y is odd, then x and y are of opposite parity.

          3.51. Let x ? Z. Use one or two lemmas to prove that
3.52. Give a direct proof of the following: Let x ? Z. If 11x – 5 is odd, then x is even.
3.53. Let x, y ? Z. Prove that if x + y is odd, then x and y are of opposite parity.

Added by Laura C.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Drew Scalzo

10/16/2022

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Step 1: Assume that x is odd. Show more…

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3.51. Let x ∈ Z. Use one or two lemmas to prove that if x is odd, then x² is even. 3.52. Give a direct proof of the following: Let x ∈ Z. If 11x – 5 is odd, then x is even. 3.53. Let x, y ∈ Z. Prove that if x + y is odd, then x and y are of opposite parity.