Consider the following statement: ∀ integers n, if n2 is even then n is even. Which of the following are equivalent ways of expressing this statement? a. All integers have even squares and are even. b. Given any integer whose square is even, that integer is itself even. c. For all integers, there are some whose square is even. d. Any integer with an even square is even. e. If the square of an integer is even, then that integer is even. f. All even integers have even squares

Question

Bryson

Mathematics

8 May, 08:03

Consider the following statement: ∀ integers n, if n2 is even then n is even. Which of the following are equivalent ways of expressing this statement? a. All integers have even squares and are even. b. Given any integer whose square is even, that integer is itself even. c. For all integers, there are some whose square is even. d. Any integer with an even square is even. e. If the square of an integer is even, then that integer is even. f. All even integers have even squares

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Answers (1)

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Jillian Spence · Answer 1

B, D, E, F.

Step-by-step explanation:

In the statement, the square of an even integer is even. From the options provided, we have to select the ones that provide similar ways of expressing this.

Options B, D, E, F provided with the question and reproduced below convey the same statement in different ways:

B: Given any integer whose square is even, that integer is itself even.;

D: Any integer with an even square is even.;

E: If the square of an integer is even, then that integer is even and

F: All even integers have even squares.