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?

- 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.

- 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.