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AssignmentMultiple Choice

Logic and Reasoning

Question 1 • (A. Costello)WCA 5324 Geometry 1st Nine Weeks 26-27

Which statement is true regarding the given logical statement?If a number is a square number greater than 1, then it has at least one factor other than 1 and itself.

Answer
A
An equivalent statement is "all numbers having at least one factor other than 1 and itself are square numbers."
B
The hypothesis is "a number is a square number greater than 1."
C
The conclusion is "a number is a square number greater than 1."
D
A counterexample for this conditional statement is 49.

Explanation

In a conditional statement of the form “if P, then Q,” the hypothesis is the part after “if,” and the conclusion is the part after “then.” Here, the hypothesis is “a number is a square number greater than 1,” so choice B is true. Choice D is not a counterexample because 49 is a square greater than 1 and has factors other than 1 and itself, such as 7.

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