Lesson: Law of Syllogism
In this lesson, we will learn how to draw conclusions from two conditional statements when the conclusion of one statement is the hypothesis of the other.
Sample Question Videos
Worksheet: 3 Questions • 2 Videos
Hannah knows that the following two statements are true:
- If a student does not complete their homework, they will get detention.
- If a student gets detention, they will be late home.
Jacob got detention and was late home.
Can we conclude that he did not complete his homework?
Jennifer did not do her homework.
Can we conclude that she was late home?
Consider the following two statements:
Statement 1: If A is true, then B is true.
Statement 2: If B is true, then C is true.
If both statements are true, then the law of syllogism tells us that we can write a third true statement:
Statement 3: If A is true, then C is true.
Given statements 3 and 4 below, which of the following statements is also true?
Statement 3: If is odd, then both and are odd.
Statement 4: If both and are odd, then is even.
Statement 5: If a shape is a square, then it has a right angle.
Statement 6: If a shape is a square, then it has a pair of parallel sides.
Shape has a right angle and a pair of parallel sides. What can we conclude about shape from the given statements?
Which of the following statements follows logically from statements A and B?
- If Amir misses the bus, then he will be late for work.
- If Amir is late for work, then he will not be paid a bonus.