ConditionalStatements

Conditional StatementConditional Statement

An “if” … “then” ….(may be true or false)

Example:If you eat Doritos, then you will have bad breath.

Conditional StatementConditional Statement

If p, then q.

HypothesisHypothesis

The part of a conditional statement after the “if”

If you stick your finger in the electrical socket, then I will laugh.

If you stick your finger in the electrical socket, then I will laugh.

ConclusionConclusion

The part of a conditional statement after the “then”

If you stick your finger in the electrical socket, then I will laugh.

If you stick your finger in the electrical socket, then I will laugh.

ConverseConverseWhen you switch the hypothesis

and conclusion of a conditional statement.

(The “If” and “then” do not move)

If you stick your finger in the electrical socket, then I will laugh.

If you stick your finger in the electrical socket, then I will laugh.

If I laugh, then you stuck your finger in the electrical socket.

Converse:

Conditional:

ConverseConverseWhen you switch the hypothesis

and conclusion of a conditional statement.

(The “If” and “then” do not move)

If p, then q.

If q, then p.Converse:

Conditional:

Write the converse of the following statement.

If you eat Doritos, then you have bad breath.

Conditional:

If you have bad breath, then you ate Doritos.

Converse:

If you eat Doritos, then you have bad breath.

InverseInverseWhen you negate the hypothesis

and conclusion of a conditional statement.

If you stick your finger in the electrical socket, then I will laugh.

If you stick your finger in the electrical socket, then I will laugh.

If you do not stick your finger in the electrical socket, then I will not laugh.

Inverse:

Conditional:

InverseInverseWhen you negate the hypothesis

and conclusion of a conditional statement.

If p, then q.

If ~p, then ~q.Inverse:

Conditional:

Write the inverse of the following statement.

If you shave your head, then you will look like Britney Spears.

Conditional:

If you do not shave your head, then you will not look like Britney Spears.

Inverse:

If you shave your head, then you will look like Britney Spears.

ContrapositiveContrapositiveWhen you switch AND negate the

hypothesis and conclusion of a conditional statement.

(The “If” and “then” do not move)

If you stick your finger in the electrical socket, then I will laugh.

If you stick your finger in the electrical socket, then I will laugh.

If I do not laugh, then you did not stick your finger in the electrical socket.

Contrapositive:

Conditional:

ContrapositiveContrapositiveWhen you switch AND negate the

hypothesis and conclusion of a conditional statement.

(The “If” and “then” do not move)

If p, then q.

If ~q, then ~p.Contrapositive:

Conditional:

Write the contrapositive of the following statement.

If you like enchiladas, then we can be best friends.

Conditional:

If we are not best friends, then you do not like enchiladas.

Contrapositive:

If you like enchiladas, then we can be best friends.

False StatementFalse StatementAny statement that can

be disproved.

All red heads are un-athletic.

False.

CounterexampleCounterexampleAn example that disproves a

false statement.Example:

All red heads are un-athletic.

False.

Counterexample:

Shaun White Andy Dalton Blake Griffin

Rewrite the statement into a conditional statement then determine if the following is true or false; if false, give a counterexample.

All squares are rectangles.

Conditional Statement:

True or False:

If it is a square, then it is a rectangle.

True.

Rewrite the statement into a conditional statement then determine if the following is true or false; if false, give a counterexample.

All rectangles are squares.

Conditional Statement:

True or False:

If it is a rectangle, then it is a square.

False.

Not all rectangles have side lengths thatare the same.

Counterexample:

Law of Syllogism

If a=b

then a = cand b=c

Law of Syllogism

Marsha is older than Jan.

Then Marsha is older than Cindy.

Jan is older than Cindy.

Law of Syllogism

Mrs. Wenter is a nerd.

then Mrs. Wenter loves math.

All nerds love math.