10.	+Biconditional+Statements


 * By Robert Geerlof and Dylan Feinstein

You may be asking yourself... what are biconditional statements? We are here to tell you exactly what they are.**

Definition: A statement that if one of the propositions is true if and only if the other is true.

Rules: 1)You may only write a true biconditional statement if the conditional statement and converse are both true. 2) If one or both of the conditional statement and converse are false, then you write a counterexample. 3) A biconditional statement __//**ALWAYS**//__ is a "if and only if" statement.

Examples:  1. Conditional Statement- If you are having McDonald's, then you are loving it. **This is true.** Converse- If you are loving it, then you are having McDonald's. **This is true.** Inverse- If you are not having McDonald's, then you are not loving it. Contrapositive- If you are not loving it, then you are not having McDonald's
 * __BICONDITIONAL: You are having McDonald's if and only if you are loving it.__**

2. Conditional Statement- If the candidate becomes president he must win the election. **This is true.** Converse- If the candidate wins the election, he becomes president. **This is true.** Inverse- If the candidate does not become president, he does not win the election. Contrapositive- If the candidate does not win the election, he does not become president. __**BICONDITIONAL: The candidate becomes president if and only if he wins the election.**__

3. Conditional Statement- If the player wins a trophy, he won the game. **This is true.** Converse- If the player won the game, he wins the trophy. **This is true.** Inverse- If the player does not win the trophy, he does not win the game. Contrapositive- If the player does not win the game, he does not win the trophy.
 * __BICONDITIONAL The player wins a trophy if and only if he wins the game.__**

EXAMPLE OF ONE THAT IS NOT ALL TRUE 1. Conditional Statement- If the man gets the job, he will make money. **This is true.** Converse- If the man makes money, he gets the job. **This is false** Inverse- If the man does not get the job, he will not make money. Contrapositive- If the man does not make money, he will not get the job. __**Counterexample- The man can make money without getting the job. Because the converse is false, you cannot make a true biconditional statement.**__

Short Video On Biconditional Statements:



Excellent Websites To Enjoy:

**[|Explore Learning]** - This website is a gizmo that gives you examples of biconditional statements and counterexamples.

[|Tutor Vista] -This website is helpful and tells you how to do all of the steps.

- This website gives defintions of biconditional statements and examples of them.
 * [|Atheism]**