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.

Question

Mathematics

Estrella Day

19 June, 15:44

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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Answers (1)

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Williamson · Answer 1

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.

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

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.