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 𝑎 𝑏 is odd, then both 𝑎 and 𝑏 are odd.

Statement 4: If both 𝑎 and 𝑏 are odd, then 𝑎 + 𝑏 is even.

  • AIf 𝑎 is odd, then both 𝑎 + 𝑏 and 𝑎 𝑏 are odd.
  • BIf 𝑎 + 𝑏 is even, then 𝑎 𝑏 is odd.
  • CIf 𝑎 𝑏 is odd, then 𝑎 + 𝑏 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 𝑄 has a right angle and a pair of parallel sides. What can we conclude about shape 𝑄 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.

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