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### 2.1 Conditional Statements

Chapter 2: Reasoning and Proof

Conditional: another name for an if-then statement

“If you are not completely satisfied, then your money will be refunded.”

Hypothesis: the part following the if

Conclusion: the part following the then

Identifying the Hypothesis and Conclusion

Identify the hypothesis and the conclusion of this conditional statement:

“If today is the first day of fall, then the month is September.”

Hypothesis:

Conclusion:

Today is the first day of fall

The month is September

Writing a Conditional

Write each sentence as a conditional:

- A rectangle has four right angles.
- A tiger is an animal.
- An integer that ends with 0 is divisible by 5.
- A square has four congruent sides.

If a figure is a rectangle, then it has four right angles.

If something is a tiger, then it is an animal.

If an integer ends with 0, then it is divisible by 5.

If a figure is a square, then it has four congruent sides.

Truth Value

A conditional can have a truth value of true or false.

To show that a conditional is true, show that every time the hypothesis is true, the conclusion is also true.

To show that a conditional is false, you only need to find one counterexample.

Finding a Counterexample

Show that this conditional is false by finding a counterexample:

If it is February, then there are only 28 days in the month.

Counterexample: There are 29 days in a leap year.

Finding a Counterexample

Show that this conditional is false by finding a counterexample:

If the name of a state contains the word New, then the state borders an ocean.

Counterexample: New Mexico

Using a Venn Diagram

Draw a Venn diagram to illustrate this conditional:

“If you live in Chicago, then you live in Illinois.”

Residents of

Illinois

Residents

of Chicago

Using a Venn Diagram

Draw a Venn diagram to illustrate this conditional:

“If something is a Cocker Spaniel, then it is a dog.”

Dogs

Cocker

Spaniels

Converse: switches the hypothesis and the conclusion

Conditional:

If two lines intersect to form right angles, then they are perpendicular.

Converse:

If two lines are perpendicular, then they intersect to form right angles.

Writing a converse

Conditional:

If two lines are not parallel and do not intersect, then they are skew.

Converse:

If two lines are skew, then they are not parallel

and do not intersect.

Finding the Truth Value of a Converse

Conditional:

If a figure is a square, then it has four sides.

Converse:

If a figure has four sides, then it is a square.

*Is this statement true?

No, a rectangle also has four sides, so the converse is false.

*Look in book, page 70, Summary box for Symbolic Form

Homework

Pg 71 2 – 34 even, 64 – 67all

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