Answered

Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

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.

Sagot :

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."
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.