Statements that areStatements that are

Conditional with aConditional with a

hypothesishypothesis and a and a

conclusionconclusion..

TheThe If If part of the part of the

statement is the statement is the

Hypothesis, and theHypothesis, and the

ThenThen part of the part of the

statement is the statement is the

Conclusion.Conclusion.

If you are a champion then you are afraid to lose.

A Champion is afraid to lose.

Examples

Statement If-Then Form

Babies are small. If a person is a baby, then they are small.

A triangle has three sides.

If a shape is a triangle, then it has three sides.

Snakes are despised. If an animal is a snake, then it is despised.

If the sun is up then it is morning.

If the sun is up then it can be in the afternoon.

Conditional Conditional Statements have a Statements have a truth valuetruth value, of true , of true or false. or false. To prove To prove that a statement is that a statement is false it only takes false it only takes oneone counterexamplecounterexample which shows that the which shows that the hypothesis is hypothesis is truetrue and the conclusion is and the conclusion is falsefalse..

A Venn diagram A Venn diagram can be used can be used to illustrate to illustrate conditional conditional statements.statements.

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

Residents of Illinois

Residents ofChicago

Take the original statement and switch the hypothesis and the conclusion.

Conditional

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

Converse

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

• Conditional• 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.• Conditional• If something is a cocker spaniel,

then it is a dog.• Converse• If something is a dog, then it is a

cocker spaniel.

More Examples

Symbolic Form

p → q

q → p

You Read it

If p, then q.

If q, then p.

When a conditional and its converse are true, you can combine them as a true biconditional.

ConditionalIf two angles have the same measure, then they are congruent.ConverseIf two angles are congruent, then they have the same measure.BiconditionalTwo angles have the same measure if and only if (iff ) the angles are congruent.p q

ConditionalConditional

If If anan angle is a straight angle is a straight angleangle, then , then its measure is its measure is 180º180º..

ConverseConverse

If If anan angle has a measure angle has a measure of 180ºof 180º, then , then it is a it is a straight anglestraight angle..

BiconditionalBiconditional

An angle is a straight angleAn angle is a straight angle if and only if (iff) if and only if (iff) its its measure is 180ºmeasure is 180º..

Example:

Symbolic Form: You read it:

p → q If p then q.

Symbolic Form: You read it:

p q p if and only if q.

Symbolic Form: You read it:

q → p If q then p.