Worksheet: Law of Detachment

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


Nabil 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


Decide whether the conclusion is valid.

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

Given: 𝐴 𝐵 𝐶 is an obtuse triangle.

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

  • ANot valid
  • BValid


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 𝑎 and 𝑏 are odd numbers, then 𝑎 𝑏 is odd.

Statement 2: 𝑐 and 𝑑 are odd numbers.

What can we conclude about 𝑐 𝑑 ?

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

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

Statement 4: 𝑞 is an odd number.

Can we conclude 𝑞 is prime? Why?

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

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