Lesson: Law of Detachment
In this lesson, we will learn how to use facts, rules, definitions, or properties to reach logical conclusions from given statements.
Sample Question Videos
Worksheet: 3 Questions • 2 Videos
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?
It rained on Tuesday. Can you conclude that the grass was wet on Tuesday?
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.
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 ?
Statement 3: If is an odd number, then is prime.
Statement 4: is an odd number.
Can we conclude is prime? Why?