# Worksheet: Law of Detachment

Q1:

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.

Q2:

Decide whether the conclusion is valid.

Given: If two angles in a triangle add up to 70 degrees, then the triangle is obtuse.

Given: is an obtuse triangle.

Conclusion: Two of the angles in triangle add up to 70 degrees.

• ANot valid
• BValid

Q3:

William knows that the following statement is true: If it rains today, the grass will be wet.

The grass was wet on Monday. Can you conclude that it rained on Monday?

• ANo
• BYes

It rained on Tuesday. Can you conclude that the grass was wet on Tuesday?

• AYes
• BNo