Conditional Statements

p→q
What is the contrapositive?

• q→p
• ∼p→∼q
• ∼q→∼p
• p→∼q

p→q
What is the converse?

• q→p
• ∼p→∼q
• ∼q→∼p
• p→∼q

If it is a triangle then it has three sides.
What is the hypothesis?

• it is a polygon
• it is a triangle
• it has three sides
• a triangle is a polygon

What does this mean?

• Conditional Statement
• Inverse Statement
• Converse Statement
• Contrapositive Statement

p→q
What is the inverse?

• q→p
• ∼p→∼q
• ∼q→∼p
• p→∼q

Original: If Jenny buys a guitar, then she will not buy a keyboard.
What is this? If Jenny does buy a keyboard, then she will not buy a guitar.

• Converse
• Inverse
• Contrapositive
• Negation

What is the inverse?
If Jason does not go out to dinner, then he will come to the volleyball game.

• If Jason goes out to dinner, then he will not come to the volleyball game.
• If Jason comes to the volleyball game, then he will not go out to dinner.
• If Jason comes to the volleyball game, then he will go out to dinner.
• If Jason does not go out to dinner, then he will not come to the volleyball game.

Given, "If angles are congruent, then the measures of the angles are equal." Identify the converse.

• If the measures of the angles are equal, then the angles are congruent.
• "If angles are not congruent, then the measures of the angles are not equal."
• If the measures of the angles are not equal, then the angles are not congruent.
• If the angles are not congruent, then the measure of the angles are equal.

What type of statement is this?

• Conditional

• Converse

• Inverse

• Contrapositive

• Biconditional

What type of statement is this?

• Conditional

• Converse

• Inverse

• Contrapositive

• Biconditional