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