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### Conditional Statements

Section 2-2

Objective

Students will be able to recognize conditional statements and their parts to write converses, inverses, and contrapositives of conditionals.

Conditional Statements

If-then statements are called conditional statements.

The portion of the sentence following if is called the hypothesis. The part following then is called the conclusion.

p q (If p, then q)

p

q

If it is an apple, then it is a fruit.

Hypothesis – It is an apple.

Conclusion – It is a fruit.

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

Converse q p

The converse statement is formed by switching the hypothesis and conclusion.

If it is an apple, then it is a fruit.

Converse: If it is a fruit, then it is an apple.

The converse may be true or false.

Underline the hypothesis and circle the conclusion for each conditional statement, then write the converse.

- If you are an American citizen, then you have the right to vote.
- If a figure is a rectangle, then it has four sides.

Write each sentence as a conditional statement.

- A point in the first quadrant has two positive coordinates.

If a point is in the first quadrant, then it has two positive coordinates.

- Thanksgiving in the U.S. falls on the fourth Thursday of November.

If it is Thanksgiving in the U.S., then it is the fourth Thursday of November.

Using a Venn Diagram to illustrate a conditional

Illinois Residents

Chicago Residents

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

Get a Partner!

- Each of you need to write 5 conditional statements and draw 5 venn diagrams
- Trade papers
- Write the converse of each conditional statement your partner wrote.

Biconditionals

- Remember: If your original conditional statement is true and your converse is true, then you can write a biconditional. p↔q read as “p if and only if q” we can shorten it to “p iff q”.
- When either or both of your condition and the converse is false, then you must write a counter example. Why is it false?
- See page 78 for sample problems!

The new stuff for today:

negation – the denial of a statement (the opposite)

Ex. “An angle is obtuse.”

Negation – “An angle is not obtuse.”

Inverse ~p ~q

An inverse statement can be formed by negating both the hypothesis and conclusion.

If it is an apple, then it is a fruit.

Inverse: If it is not an apple, then it is not a fruit.

The inverse may be true or false.

Contrapositive ~q ~p

A contrapositive is formed by negating the hypothesis and conclusion of the converse.

If it is an apple, then it is a fruit.

Contrapositive: If it is not a fruit, then it is not an apple.

The contrapositive of a true conditional is true and of a false conditional is false.

Truth Table

T

F

T

T

T

F

T

T

T

T

F

T

T

T

F

T

T

F

F

F

T

T

T

F

T T

T F

F T

F F

Which columns are congruent? These are called equivalent statements, because they have the same truth values!

Assignment:

- P. 93 (15-45) x’s of 3
- Ask me about the OPTIONAL project!

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