Blog Entry #2

35.) Write the definition of a biconditional statement as a biconditional statement. Use the conditional and converse within the statement to explain why your biconditional is true. 

Biconditional: A statement is a biconditional if and only if it is written in the form "p if and only if q."
Conditional: If a statement is written in the form "p if and only if q," then it is a biconditional statement. (Truth Value: True)
Converse: If a statement is written in the form "p if and only if q," then it is a biconditional. (Truth Value: True

The biconditional is true since both the conditional and the converse are true.

36.) Use the definition of an angle bisector to explain what is meant by the statement "A good definition is reversible."

Definition: An angle bisector is a ray that divides an angle into two congruent angles.
A good definition is reversible since its statement has true value as a conditional statement and as a converse.
Biconditional: A ray is an angle bisector if and only if it divides an angle into two congruent angles.

Conditional: If a ray is an angle bisector, then it divides an angle into two congruent angles; True

Converse: If a ray divides an angle into two congruent angles, then it is an angle bisector; True

The definition of an angle is a good definition because it is reversible. Both conditional and converse are true, so that means the whole definition is true. 

41.) Write the two conditional statements that make up the biconditional "You will get a traffic ticket if and only if you are speeding." Is the biconditional true or false? Explain your answer.

Conditional: If you get a traffic ticket, then you are speeding.
Truth Value: False; you can get a ticket for other issues, like passing a red light.

Converse: If you are speeding, then you get a traffic ticket. 
Truth Value: False; You only get a traffic ticket when caught speeding. Those who don't get caught speeding does not get a traffic ticket.

The biconditional is false because both conditional and converse were false.
For the biconditional to be true, the conditional and converse have to both be true. But since they are both not true, the biconditional is false.