Conditional Statements, Converse, and Counterexamples

Warm Up:

3x 9x + 2

94°

67°

93°

xSolve for x in both figures.

Conditional Statement Conditional statement has two parts, hypothesis

and a conclusion.

hypothesis conclusionIf ____________, then____________.

If the man eats donuts, then he must be a policeman.

If the animal has four legs, then it must be a dog.

If the bug stings, then it must be a wasp.

Rewrite in If-Then form

Two points are collinear if they lie on the same line.

A seal swims.

-Two points are collinear- Lie on the same line

If two points lie on the same line, then they are collinear.

- Seal (animal)- Swims

If the animal is a seal, then it swims.

Rewrite in If-Then form

A number divisible by 9 is also divisible by 3.

A square has four sides.

-Number divisible by 9- Divisible by 3

If a number is divisible by 9, then it is also divisible by 3.

- Square- Four sides

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

What is the Converse?

If __________, then_________.hypothesis conclusion

Conditional Statement

conclusion hypothesis

If the man eats donuts, then he must be a policeman.

Converse Statement

If he is a policeman, then he must eats donuts.

If the animal has four legs, then it must be a dog.

If it is a dog, then it must have four legs.

Converse or Conditional: which is true?

State whether each sentence is true or false.

True

False

If you live in Los Angeles, then you live in California.

If you live in California, then you live in Los Angeles.

If today is Wednesday, then tomorrow is Thursday.If tomorrow is Thursday, then today is Wednesday.

True

True

Write the Converse? qp

Counterexample

An example that proves a statement is FALSE

If you live in California, then you live in Los Angeles.

Counterexample: Ms. McGregor lives in Huntington Beach, California.

Find a Counterexample for the following:

If the animal has teeth, then it is a shark.

If the shape has four right angles, then it is a square.

TRUE FALSE

TRUE

FALSE

Find a Counterexample for the following:

All teachers are boring.

Mary’s counterexample is her best friend Alexis that is a senior. They are never bored when they are together.

Why isn’t this a proper counterexample?

Joe’s counterexample is Mrs. Lara. She gives tons of homework!

Why doesn’t this count as a counterexample?

Formal Notation

Conditional Statement If (hypothesis), then (conclusion). p = hypothesis and q = conclusion

If p, then q.p implies qp q→

Formal Notation

Converse Statement If (conclusion), then (hypothesis).

If q, then p.q implies pq p→

Find a Counterexample

If a something has four wheels, then it is used for transportation.

If an animal has spots, then it is a leopard.

Two lines in a plane always intersect in exactly one point.

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