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Worksheet: Law of Detachment


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 π‘Ž and 𝑏 are odd numbers, then π‘Ž 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: π‘ž is an odd number.

Can we conclude π‘ž is prime? Why?

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


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 𝐡 𝐢 is an obtuse triangle.

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

  • ANot valid
  • BValid


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