2-1 Conditionals

2-1 Conditionals

An "if-then" statement is called a CONDITIONAL. The "if" part is the hypothesis and the "then" part is the conclusion.

Ex. If I am tired, then I yawn.

The hypothesis is "I am tired" and the conclusion is "I yawn."

Multiple Choice

What is the hypothesis in "If you live in Reading, then you live in PA."

• You live in Reading.

• You live in PA.

• You live in the USA.

Multiple Choice

What is the conclusion in "If you live in Reading, then you live in PA?"

• You live in Reading.

• You live in PA.

• You live in the USA

Conditionals aren't always written in "if...then" form. In this next section, you will practice rewriting them.

Ex. "All cats are adorable. " The hypothesis is that you have a cat and the conclusion is that it's adorable. So it would be written as "If an animal is a cat, then it is adorable."

Multiple Choice

Rewrite "All games are fun" in if-then form.

• If something is a game, then it is fun.

• If something is fun, then it is a game.

Multiple Choice

Rewrite in "if-then" form: "Every person born in Philly loves cheese steaks."

• If a person is born in Philly, then they love cheesesteaks.

• If a person loves cheesesteaks, then they are born in Philly.

When you flip the hypothesis and conclusion, you create the CONVERSE of the original statement.

Ex. The converse of "If I am happy, then I smile" is "If I smile, then I am happy."

Multiple Choice

Find the converse of "If I am in Mrs. Vargo's period 2 class, then I am taking geometry."

• If I am taking geometry, then I am in Mrs. Vargo's period 2 class.

• If I am not in Mrs. Vargo's period 2 class, then I am not taking geometry.

• If I am not taking geometry, then I am in Mrs. Vargo's period 2 class.

Multiple Choice

Find the converse of "If you are talking, then I am not listening."

• If you aren't talking, then I am listening.

• If I am not listening, then you are talking.

• If I am listening, then you are not talking.

If you take the opposite of the hypothesis and the opposite of the conclusion, then you create the INVERSE of the original conditional.

Ex. The inverse of "If I eat chocolate, then I'm happy" is "If I don't eat chocolate, then I'm not happy."

Multiple Choice

What is the inverse of "If an angle is right, then it measures 90^o?"

• If an angle measures 90^o,then it is right.

• If an angle isn't right, then it doesn't measure 90^o.

• If an angle doesn't measure 90^o, then it isn't a right angle.

When you negate both statements AND switch the hypothesis and conclusion, you create the CONTRAPOSITIVE.

Ex. The contrapositive of "If you live in the city, then you ride the subway" is "If I don't ride the subway, then I don't live in the city."

Multiple Choice

What is the contrapositive of "If a point is a midpoint, then it divides the segment into two congruent segments?"

• If a point isn't a midpoint, then it doesn't divide the segment into two congruent segments.

• If a point doesn't divide a segment into two congruent segments, then it isn't the midpoint.

• If a point divides a segment into two congruent segments, then it is the midpoint.

Under what conditions is the if-then relationship true? A better way to word this is when is it false. It is false only when there is an instance when the hypothesis is true YET the conclusion is false.

• Ex. "If I live in PA, then I live in Reading." This if-then is false. An example of why it's false would be any person who lives in PA (hypothesis is true) and doesn't live in Reading (conclusion is false).

Another example would be "If you own a car, then you have a car loan." This is not true. An example of why would be someone who owns a car (hypothesis is true) and doesn't have a car loan (conclusion is false).

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Multiple Choice

This statement is false. "If an angle is less than 180^o, then it is acute." Which is an example showing why it's false?

• m<X is 90^o and is not acute.

• m<X is 80^o and is acute.

• m<X is 200^o and is not acute.