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Given:(1) The following argument is valid:p -> qNOT p______Therefore NOT q(2) Let a and b be two positive integers such that a > 1, b > 1, and a > b.SQRT(SQRT(a)) - SQRT(SQRT(b)) is always an irrational number.Select one of the following choices:Question 1Answera.(1) and (2) are False.b.(1) and (2) are True.c.(1) is True and (2) is False.d.(1) is False and (2) is True.

Question

Given:(1) The following argument is valid:p -> qNOT p______Therefore NOT q(2) Let a and b be two positive integers such that a > 1, b > 1, and a > b.SQRT(SQRT(a)) - SQRT(SQRT(b)) is always an irrational number.Select one of the following choices:Question 1Answera.(1) and (2) are False.b.(1) and (2) are True.c.(1) is True and (2) is False.d.(1) is False and (2) is True.

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Solution

The correct answer is c. (1) is True and (2) is False.

Here's why:

(1) The argument is valid. This is a standard form of logical argument known as Modus Tollens. If p implies q (p -> q), and we know that p is not true (NOT p), then we can conclude that q is not true (NOT q).

(2) This statement is false. The square root of a square root of a number can be either rational or irrational, it depends on the number. For example, if a = 16 and b = 9, then SQRT(SQRT(a)) - SQRT(SQRT(b)) = 2 - 1.5 = 0.5, which is a rational number.

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