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