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Determine whether each statement is true or false. For each true statement, give a direct proof as justification. For each false statement, give a counterexample as justification. i If z+ y is an even integer, then x and y are both even integers. ii If r = y, then x=y. iii The mean of two even numbers is even. iv If x and y are even integers, then z+y is an even integer.

Determine whether each statement is true or false. For each true statement, give a direct proof as justification. For each false statement, give a counterexample as justification. i If z+ y is an even integer, then x and y are both even integers. ii If r = y, then x=y. iii The mean of two even numbers is even. iv If x and y are even integers, then z+y is an even integer.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.5: Mathematical Induction
Problem 41E
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discrete math help please say st oupp wsan s . Mcutne w LE Wu prane. Please use the following definitions of even and odd numbers: • An integer a is even if there exists an integer z with a = 2z. • An integer a is odd if there exists an integer z with a = 2: +1. Your proofs may use the fact that every integer is either even or odd, but not both. Determine whether each statement is true or false. For each true statement, give a direct proof as justification. For each false statement, give a counterexample as justification. i If z+y is an even integer, then x and y are both even integers. ii If r = y, then x=y. iii The meanof two even numbers is even. iv If x and y are even integers, then r+y is an even integer. 'We avoid using the term 'average' as it can refer to a few different measures of the 'middle' of a set of numbers.
Transcribed Image Text:discrete math help please say st oupp wsan s . Mcutne w LE Wu prane. Please use the following definitions of even and odd numbers: • An integer a is even if there exists an integer z with a = 2z. • An integer a is odd if there exists an integer z with a = 2: +1. Your proofs may use the fact that every integer is either even or odd, but not both. Determine whether each statement is true or false. For each true statement, give a direct proof as justification. For each false statement, give a counterexample as justification. i If z+y is an even integer, then x and y are both even integers. ii If r = y, then x=y. iii The meanof two even numbers is even. iv If x and y are even integers, then r+y is an even integer. 'We avoid using the term 'average' as it can refer to a few different measures of the 'middle' of a set of numbers.
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