In this worksheet, we will practice using facts, rules, definitions, or properties to reach logical conclusions from given statements.

**Q3: **

Consider the following two statements.

Statement 1: If A is true, then B is true.

Statement 2: A is true.

If both statements are true, then the law of detachment allows us to conclude that B is true.

Statement 1: If and are odd numbers, then is odd.

Statement 2: and are odd numbers.

What can we conclude about ?

- AIt is even.
- BWe cannot conclude anything.
- CIt is odd.

Statement 3: If is an odd number, then is prime.

Statement 4: is an odd number.

Can we conclude is prime? Why?

- ANo, because statement 3 is not a true statement.
- BNo, because is not .
- CYes, it follows from the law of detachment.