Worksheet: Law of Syllogism

In this worksheet, we will practice drawing conclusions from two conditional statements when the conclusion of one statement is the hypothesis of the other.

Q1:

Rania 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.

Bassem got detention and was late home.

Can we conclude that he did not complete his homework?

• ANo
• BYes

Engy did not do her homework.

Can we conclude that she was late home?

• AYes
• BNo

Q2:

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.

• AIf is odd, then both and are odd.
• BIf is even, then is odd.
• CIf is 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?

• AWe cannot conclude anything.
• BIt is a square.

Q3:

Which of the following statements follows logically from statements A and B?

1. If Amir misses the bus, then he will be late for work.
2. If Amir is late for work, then he will not be paid a bonus.
• AIf Amir was not paid a bonus, then he missed the bus.
• BIf Amir is late for work, then he missed the bus.
• CIf Amir was not paid a bonus, then he was late for work.
• DIf Amir misses the bus, then he will not be paid a bonus.