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What is the inverse of the following conditional statement?

"If a number is a prime number, then it has no factors other than one and itself."

A. If a number is not a prime number, then it has factors other than one and itself.
B. If a number has no factors other than one and itself, then it is a prime number.
C. A number is a prime number if and only if it has no factors other than one and itself.
D. If a number has factors other than one and itself, then it is not a prime number.



Answer :

GinnyAnswer
To find the inverse of a conditional statement, we negate both the hypothesis (the "if" part) and the conclusion (the "then" part).

The original statement is: "If a number is a prime number, then it has no factors other than one and itself."

Negate both parts:
- The hypothesis (a number is a prime number) becomes: a number is not a prime number.
- The conclusion (it has no factors other than one and itself) becomes: it has factors other than one and itself.

By combining these negations, the inverse of the statement is: "If a number is not a prime number, then it has factors other than one and itself."

So, the correct answer is:
"If a number is not a prime number, then it has factors other than one and itself."
brittneegiesler
A. If a number is not a prime number, then it has factors other than one and itself.

To find the inverse of a conditional statement, you negate both the hypothesis and the conclusion. The original statement is:

"If a number is a prime number, then it has no factors other than one and itself."

Let's denote:
-p: "a number is a prime number"
-q: "it has no factors other than one and itself"

The original statement is p→q.

The inverse of this statement is ¬p→¬q
-¬p: "a number is not a prime number"
-¬q: "it has factors other than one and itself"

So, the inverse is: "If a number is not a prime number, then it has factors other than one and itself."

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