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(a) If m, n are odd integers, then mn is an odd integer. (b) If m, n are integers and mn is even, then m is even or n is even. (c) If z, y are real numbers and x +y is irrational, then z is irrational or y is irrational.

(a) If m, n are odd integers, then mn is an odd integer. (b) If m, n are integers and mn is even, then m is even or n is even. (c) If z, y are real numbers and x +y is irrational, then z is irrational or y is irrational.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Mathematical Proofs Exercise** 5. Prove each of the following statements: (a) If \( m, n \) are odd integers, then \( mn \) is an odd integer. (b) If \( m, n \) are integers and \( mn \) is even, then \( m \) is even or \( n \) is even. (c) If \( x, y \) are real numbers and \( x + y \) is irrational, then \( x \) is irrational or \( y \) is irrational.
Transcribed Image Text:**Mathematical Proofs Exercise** 5. Prove each of the following statements: (a) If \( m, n \) are odd integers, then \( mn \) is an odd integer. (b) If \( m, n \) are integers and \( mn \) is even, then \( m \) is even or \( n \) is even. (c) If \( x, y \) are real numbers and \( x + y \) is irrational, then \( x \) is irrational or \( y \) is irrational.
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