BICONDITIONALS

When is a conditional statement false?

The only time a conditional statement is false is if you can find a time when the “IF” part is true and the “THEN” part is false

Example

If the school is closed, then it is Saturday.There is another day when the school is closed but it is not Saturday:

Sunday

Therefore, this conditional statement is false.

Example

If you teach geometry, then your name is Mrs. Wenter.

There is another teacher who teaches geometry but their name is not Mrs. Wenter

Mr. Mottola

Therefore, this conditional statement is false.

Think about science…

Biconditional

Biconditional – the combination of a true statement and its true converse. Rewritten with the combining phrase "if and only if".

Example of biconditionalConditional: If x is a prime number, then x has exactly two factors. TrueConverse:If x has exactly two factors, then x is a prime number. True

Biconditional:X is a prime number if and only if x has exactly two factors.

Example of biconditionalConditional: If I am alive, then my heart is beating

TrueConverse:If my heart is beating, then I am alive.

True

Biconditional:I am alive if and only if my heart is beating.