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3 March, 16:04

Consider the proposition " There exists an integer n such that for all integers m, m

a) Write the negation of the proposition (in English).

b) Determine if the proposition is true or if the negation is true. Give a reason for your choice.

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  1. 3 March, 18:16
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    a) "There is no integer n such that for all integers m, m
    b) The proposition is false and its negation true.

    Step-by-step explanation:

    a)

    The negation of the proposition is

    "There is no integer n such that for all integers m, m
    b)

    It is easy to prove that the proposition is false.

    If there existed such an integer n, then since n+1 is an integer, n+1 < n, which is a contradiction.

    So such an integer n cannot exist.

    Since the proposition is false, its negation is true.
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