Sure, let's work through this step by step.
First, we need to understand the original conditional statement:
Original Statement:
"If a number is a prime number, then it has no factors other than one and itself."
In logical terms, this can be written as:
P → Q, where:
- P: A number is a prime number.
- Q: The number has no factors other than one and itself.
To find the inverse of this conditional statement, we negate both the hypothesis (P) and the conclusion (Q). In logical terms, the inverse is written as:
¬P → ¬Q, where:
- ¬P: A number is not a prime number.
- ¬Q: The number has factors other than one and itself.
So, the inverse statement becomes:
"If a number is not a prime number, then it has factors other than one and itself."
Among the options given:
1. If a number is not a prime number, then it has factors other than one and itself.
2. If a number has no factors other than one and itself, then it is a prime number.
3. A number is a prime number if and only if it has no factors other than one and itself.
4. If a number has factors other than one and itself, then it is not a prime number.
The correct inverse statement is:
Option 1: If a number is not a prime number, then it has factors other than one and itself.
So, the correct answer is Option 1.
