WARMUP If an integer ends with 0, then

the integer is divisible by 2.

What is the truth value of the above conditional?

What is the converse? What is the truth value of the

converse?

Go over hmwk 2-1

2.2 BICONDITION

ALS/DEFINITIONS

10/3

LEARNING TARGET

I can write a biconditional given a conditional and it’s converse.

Biconditional: When the conditional and its converse are both true, you can combine them into one statement called a biconditional. You connect them with the phrase if and only if.

Writing a biconditionalFirst, determine if the conditional and converse are true. They both must be true

Second, go to the conditional, and take out IF from the beginning.

Third, replace the word THEN with “if and only if”

Example:

Conditional: If two angles have the same measure, then the angles are congruent

Converse: Truth Values: Biconditional:

Example:

Conditional: If three points are collinear, then they lie on the same line.

Converse: Truth Values: Biconditional:

Separating a biconditionalThis is taking a biconditional and coming up with the conditional and it’s converse.

Example

Biconditional: A number is divisible by 3 if and only if the sum of its digits is divisible by 3

Conditional: Converse:

Example

Biconditional: A number is prime if and only if it has two distinct factors, 1 and itself

Conditional: Converse:

PROPERTIES OF GOOD DEFINITIONS: Use clearly understood or already defined terms.

Are precise. Avoid general words such as some, sort of, big, small.

Are reversible. You can write a good definition as a biconditional.

WRITING A DEFINITION AS A BICONDITIONAL Definition: Perpendicular lines are two

lines that intersect to form right angles Conditional: if two lines are

perpendicular, then they intersect to form right angles

Converse: if two lines intersect to form right angles, then they are perpendicular

Biconditional: Two lines are perpendicular if and only if they intersect to form right angles

Definition: A right angle is an angle whose measure is 90

Conditional: Converse: Biconditional:

Symbolic Form

Biconditional p q (p if and only if q)

HOMEWORK 2-2 in the Packet #1-12

HomeworkP. 78-79 # 2-22 even; 32-35