Hello! For this week I will be talking about biconditional statements. You might be asking yourself, "What exactly is a biconditional statement?" To answer your question, a biconditional statement is statement that can be written in the form "p if and only if q." A biconditional statement is when you combine a conditional statement and it's converse.
I answered pages 100-101 and did numbers 35,36, and 41. For #35, the biconditional statement is: A statement is a biconditional statement if and only if it can be written in the form "p if and only if q." I took the definition of a biconditional statement and then wrote it in the form of a biconditional statement. The conditional statement is: If a statement is a biconditional statement, then it can be written in the form "p if and only q." A conditional statement is written in the form "if p, then q". For the converse: If a statement can be written in the form "p if and only if q", then it is a biconditional statement. The converse is when you reverse the conditional statement, it is written in the form "if q, then p". Since both the converse and conditional statements are true, the biconditional is true.
#36 .) Definition: a ray that divides an angle into two congruent angles. The conditional statement is: if a ray is an angle bisector, then it divides an angle into two congruent angles. This conditional statement is true. Now the reversed version or converse is: If a ray divides an angle into two congruent angles, then it is an angle bisector. The converse is also true. A good definition is one where it is either reversed and forward and you still have a true value.
#41.). The 1st conditional statement: if you get a traffic ticket, then you are speeding. This conditional statement is false. The 2nd conditional statement: if you are speeding, then you get a traffic ticket. This 2nd conditional statement is true. If you want your biconditional to be true, your conditional and converse both have to be true as well. But here, since the conditional statement is false, the biconditional is also false. The 1st conditional statement is false because you can get a traffic ticket for going to slow or violating other laws, not just speeding.
A good definition is able to be used either forward or backwards. A biconditional statement requires your ability to write a conditional statement and a converse. If you are able to properly write a conditional and converse,then you are a step closer to writing a biconditional statement. The biconditional statement also test your ability to think and look at different perspectives.
Pictures of biconditional statements:
1.) How to write biconditional statements symbolically and using words:
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