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.

a) “There is no integer n such that for all integers m, m<n”

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<n”

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.

d. 8

step-by-step explanation:

the given radical expression is:

we can rewrite this as:

we express as square numbers to get;

the exponents will now cancel out to give.

the correct answer is d

the answer is b