Conditional Statements

Learning Target: I can write converses, inverses, and contrapositives of conditionals.

·Conditional Statements are If-Then StatmentsEx. If you are not completely satisfied, then your money will be refunded.

·Hypothesis - the part following the IfEx. you are not completely satisfied

·Conclusion - the part following the ThenEx. your money will be refunded.

The letter p always represents the hypothesis.

The letter q always represents the conclusion.

Notation: p qFor a conditional, we say if p then q.Ex. If m<A=15, then <A is acute.

Identify the hypothesis and conclusion

If today is September 23, then it is Ms.Tilton's birthday

Hypothesis:

Conclusion:Today is September 23

It is Ms. Tilton's birthday

Identify the hypothesis and the conclusion of the conditional.If an angle measures 130, then the angle is obtuse.

Hypothesis:

Conclusion:

An angle measures 130

The angle is obtuse.

Writing a Conditional A rectangle has four right anglesEx. If a figure is a rectangle, then is has foud right angles.A tiger is an animalEx. If something is a tiger, then it is an animal.A square has four congruent sidesEx. If a figure is a square, then it has four congruent sides.

·Truth value - whether a conditional is true of false

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

·To show a conditional is false, you need to find a counter example.

Find a counterexample for these conditionals

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

·If an animal is a dog, then it is a beagle.

Leap Year!

Poodles are dogs, but not beagles.

Is the conditional true or false? If it is false, find a counterexample.

Ex. If a woman is Hungarian, then she is European.

Ex. If a number is divisible by 3, then it is odd.A woman can be from France and still be European.

6 is divisible by 3, but not odd.

·The converse of a conditional switches the hypothesis and the conclusion.·Write the converse of the following conditionals.1. 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.2. If two lines are perpendicular, then they intersect to form right angles.Converse: If two lines intersect to form right angles, then they are perpendicular.

Notation: q p

For a converse, we say if q then p.

Conditional: If m<A=15, then <A is acute. Converse: If <A is acute, then m<A=15.

Find the Truth Value of a Converse

Ex. Write the Converse and determine its truth value.If a figure is a square, then it has four sides.

If a figure has four sides, then it is a square. False, a rectangle has four sides, but is not a square.

The negation of a statement has the opposite truth value. The symbol ~ is used to represent negation.

Write the negation of each statement.a. <ABC is obtuse.

b. Today is not tuesday.

c. Lines m and n are perpendicular.<ABC is not obtuse

Today is Tuesday.

The inverse of a conditional statement negates both the hypothesis and the conclusion.

Notation: ~p ~q

We read this If not p, then not q.

Conditional: If m<A=15, then <A is acute.Inverse: If m<A≠15, then <A is not acute.

Write the inverse of these conditionals:a. If a figure is a square, then it is a rectangle.

b. If an angle measures 90, then it is a right angle.

If a figure is not a square, then it is not a rectangle.

If an angle does not measure 90, then it is not a right angle.

The contrapositive of a conditional switches the hypothesis and the conclusion and negates both.Notation: ~q ~pWe read this as if not q, then not p.Contional: If m<A=15, then <A is acute.Contrapositive: If <A is not acute, then m<A≠15.

Write the contrapositive of these conditionals:a. If a figure is a square, then it is a rectangle.If a figure is not a rectangle, then it is not a square.

b. If an angle measure 90, then it is a right angle.If an angle is not right, then it does not measure 90.

Equivalent statements have the same truth value.

Statement Example Truth Value

Conditional

If m<A=15, then <A is acute.

True

Converse If <A is acute, then m<A=15.

False

Inverse If m<A≠15, then <A is not acute.

False

Contrapositive

If <A is not acute, then m<A≠15.

True