BiConditional StatementsBiConditional StatementsGeometry – Section 2.2Geometry – Section 2.2

BiConditional StatementsBiConditional Statements

Biconditional Statement: Biconditional Statement: Contains the words “if and only if”Contains the words “if and only if” Same as writing the conditional Same as writing the conditional

statement and the converse at the statement and the converse at the same time.same time.

A Biconditional Statement is true in A Biconditional Statement is true in BOTH cases! Backwards and BOTH cases! Backwards and forwardsforwards

If you do not eat meat, then If you do not eat meat, then you are a vegetarian.you are a vegetarian.

Converse: If you are a Converse: If you are a vegetarian, then you do not vegetarian, then you do not eat meat.eat meat.

Biconditional Statement: Biconditional Statement: You are a vegetarian You are a vegetarian if and if and

only ifonly if you do not eat meat. you do not eat meat.

Is this True?

If you see lightening, then you If you see lightening, then you hear thunder.hear thunder. Converse: If you hear thunder Converse: If you hear thunder

then you see lightening.then you see lightening.

Biconditional Statement: Biconditional Statement:

You see lightening You see lightening if and only ifif and only if you hear thunderyou hear thunder

Is this True?

If Johnny Depp will star in Pirates of the If Johnny Depp will star in Pirates of the Caribbean II, then he won’t have to worry Caribbean II, then he won’t have to worry about money.about money.

Converse:Converse:

Biconditional Statement:Biconditional Statement:

If he doesn’t have to worry about If he doesn’t have to worry about money then Johnny Depp will star money then Johnny Depp will star in in Pirates of the Caribbean II.in in Pirates of the Caribbean II.

Is this True?

Can not be written as a biconditional statement!