What are conditionals & biconditionals?

How do you write converses, inverses, and contrapositives?

Has two parts, a hypothesis and conclusion

If, then statements If hypothesis Then conclusion

Example: If we all get our work done, then there will be no homework.

Share with the person next to you

All dogs bark.

Two angles that are a vertical pair have the same angle measure.

The measure of a straight angle is 180.

In logic, conditional statements are represented by symbols and variables.

The statement: If it is raining, then there are clouds in the

sky.

Let R = it is raining, and Let C = there are clouds in the sky.

The logic notation would be written: R C

#3 – 5, 16 - 21

The opposite of the original statement

Adds in a “not”

The negation of the sentence:

If it is raining, then there are clouds in the sky.

If it is not raining, then there are not clouds in the sky.

The car was expensive.

The game was not broken.

When the hypothesis and conclusion are switched this is called the converse.

The converse takes on a different meaning from the original statement and is not always correct.

When we took the converse of that statement, the statement was no longer true. There can be clouds and no rain.

If I get an A on the test, then my parents will take me out to eat.

If my parents took me out to eat, then I got an A on my test.

Is it true?

Can you think of a statement that the converse would be true?

The inverse is when we take the negation of the conditional statement.

If it is raining, then there are clouds in the sky.

Inverse: If it is not raining, then there are not

clouds in the sky.

Is this true?

If you beat me in the game, then I’ll scream.

If you don’t beat me in the game, then I won’t scream.

Is it true?

Negate the statement and switch the hypothesis and conclusion.

If you are a guitar player, then you are a musician.

If you are not a musician, then you are not a guitar player.

Is it true?

Original (P = Hypothesis, Q = Conclusion) PQ

Converse QP

Inverse ~P~Q

Contrapositive ~Q~P

Pairs of statements that take on the same meaning.

The original conditional statement and the contra positive are equivalent statements because they take on the same meaning.

The converse and inverse are equivalent statements also.

Original Statement If it is raining, then there are clouds

in the sky

Contrapositive If there are no clouds in the sky,

then it is not raining.

They take on the same meaning.

If and only if statements

These statements are considered true when The hypothesis and conclusion are both

true. The hypothesis and conclusion are both

false.

Notation: P Q

Two lines are perpendicular if and only if they intersect to form a right angle.

An angle is considered obtuse if and only if the angle measure is between 90 and 180

Write the following as a biconditional statement

Coplanar points are points that lie in the same plane.