Conditional Statements Vocabulary Conditional Statement A logical statement

Conditional Statements Vocabulary

Conditional Statement • A logical statement that has two parts, a hypothesis and a conclusion • EX: All cats are mammals

If-then Form • A form of a conditional statement in which the “if” part contains the hypothesis and the “then” part contains the conclusion. • EX: If an animal is a cat, then it is a mammal. • Truth Value: true!

Hypothesis • The “if” part of a conditional statement • EX: If an animal is a cat, then it is a mammal.

Conclusion • The “then” part of a conditional statement. • EX: If an animal is a cat, then it is a mammal.

Converse • Switch the hypothesis and conclusion. • EX: If an animal is a mammal, then it is a cat. • Truth Value: not true.

Inverse • Negate the hypothesis and conclusion • (keep them IN order, but add a “not”) • EX: If an animal is NOT a cat, then it is NOT a mammal. • Truth value: not true (counterexample: dog)

Contrapositive • Switch the order AND negate • EX: If an animal is not a mammal then it is not a cat. • Truth value: true!

Biconditional Statement • A statement that contains the phrase “if and only if” in between the hypothesis and conclusion. • EX: An animal is a cat if and only if it is a mammal. • Truth value: NOT true, so we can’t write this as a biconditional.

The car runs when there is gas in the tank. • If-then form: If the car runs, then there is gas in the tank (T) • Converse: (switch order) If there is gas in the tank, then the car runs (F) • Inverse: (IN order, NOT) If the car does NOT run, then there is NO gas (F) • Contrapositive: (switch, NOT) If there’s no gas, the car won’t run (T) • Biconditional(? ):

All squares are quadrilaterals • If-then form: • Converse: • Inverse: • Contrapositive: • Biconditional(? ):

Olympians are athletes • If-Then Statement • Converse • Inverse • Contrapositive • Biconditional

All girls have brown hair • If-Then Statement If someone is a girl, then they have brown hair (F) • Converse If someone has brown hair, then they are a girl (F) • Inverse If someone is NOT a girl, then they don’t have brown hair (F) • Contrapositive If someone does NOT have brown hair, then they are NOT a girl (F) • Biconditional

All triangles have 3 sides • If-Then Statement If an object is a triangle, then it has 3 sides. • Converse If an object has 3 sides, then it is a triangle. • Inverse If an object is NOT a triangle, then it does NOT have 3 sides • Contrapositive If an object does not have 3 sides then it is not a triangle. • Biconditional An object is a triangle IF AND ONLY IF it has 3 sides