Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

# Worksheet: Law of Syllogism

Q1:

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

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

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:

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?

• ANo
• BYes

Jennifer did not do her homework.

Can we conclude that she was late home?

• AYes
• BNo