1. Entry Task
Read the Solve It problem on page 89 of your book and answer the questions.
If you can read this, then you are too close.
This is an example of a conditional statement because it is an if-then statement.

2. Entry Task
The company that prints the bumper sticker at the left below accidentally reworded the original statement and printed the sticker three different ways. Suppose the original bumper sticker is true. Are the other bumper stickers true or false? Explain.

3. Conditional Statements
Lesson 2-2

4. Conditional Statements
Definition: a conditional statement is one that can be written in if-then form
Symbolically we can write it as
The hypothesis is the part p that follows if.
The conclusion is the part q that follows then.

5. The Venn diagram shows how the set of things that satisfy the hypothesis lies inside the set of things that satisfy the conclusion. q p

6. Identify the hypothesis and conclusion of the statement.
If an integer ends in zero,
then it is divisible by 5.
hypothesis
divisible by 5
integers that end in 0
conclusion

7. Write the following statement in if-then form:
Adjacent angles share a side. If two angles are adjacent, then they share a side.

8. Truth values The truth value of a conditional is either true or false
To show that it’s true, you must show that for every time the hypothesis is true, the conclusion is also true.
To show that it’s false, you just need to find one counterexample that shows the hypothesis is true but the conclusion is false.

9. Converse Converse: If tomorrow is Wednesday, then today is Tuesday.
The converse of a conditional statement switches the hypothesis and conclusion.
Original Statement: If today is Tuesday, then tomorrow is Wednesday.
Converse: If tomorrow is Wednesday, then today is Tuesday.

10. Inverse
The inverse of a conditional statement, both the hypothesis and conclusion are negated.
Original Statement: If today is Tuesday, then tomorrow is Wednesday.
Inverse: If today is not Tuesday, then tomorrow is not Wednesday.

11. Contrapositive
The contrapositive of a conditional statement is the reversal and the negations of both the hypothesis and the conclusion.
Original Statement: If today is Tuesday, then tomorrow is Wednesday.
Contrapositive: If tomorrow is not Wednesday, then today is not Tuesday.

12. If a figure is a rectangle, then it is a parallelogram.
Write the converse of the statement.
If a figure is a parallelogram, then it is a rectangle.
Write the inverse of the statement.
If a figure is not a rectangle, then it is not a parallelogram.
Write the contrapositive of the statement.
If a figure is not a parallelogram, then it is not a rectangle.
What are the truth values of these statements?

13. All tigers are mammals. Write this as a conditional statement.
If an animal is a tiger, then it is a mammal.
Write the converse of the statement.
If an animal is a mammal, then it is a tiger.
Write the inverse of the statement.
If an animal is not a tiger, then it is not a mammal.
Write the contrapositive of the statement.
If an animal is not a mammal, then it is not a tiger.

14. What’s the truth?
If a conditional statement is true, will the converse, inverse, and contrapositive also be true?
A conditional and its contrapositive always have the same truth value.
What if the original statement is false?
Logical breakdown and miscommunication

15. Snowball Activity
Write a true conditional statement on a separate sheet of paper.
Keep it school appropriate
Crumple it up and throw it across the room.
Pick up a “snowball” and read the conditional statement. Then write the converse, inverse, and contrapositive of that statement on the crumpled up paper.

16. Snowball Activity & Practice Worksheet 2-2 Conditional Statements
Homework
Snowball Activity & Practice Worksheet 2-2 Conditional Statements