1. Notes on Logic Continued
Analyze Conditional Statements
Lesson 4.3
Page 204

2. Warm – up What is the converse of the conditional statement?
If 2 lines are perpendicular, then they intersect and form a right angle (definition of perpendicular lines).
Converse: If two lines intersect and form a right angle, then they are perpendicular.
Is the conditional statement true or false?
Is the converse true or false?

3. Definition of Equivalent Statements
When two statements are both true or both false, they are called equivalent statements. *For example, definitions always produce a true conditional statement and a true converse (see previous slide). So, the definition of perpendicular lines and its converse are an example of equivalent statements. *A conditional statement and its contrapositive always have the same truth value.

4. Definition of a Biconditional Statement
A biconditional statement is the combination of a conditional statement and its converse into one statement.
The two statements are combined with the words “if and only if.” The symbol for “if and only if” is “iff.”
*This is the only time that we don’t begin the sentence with the word “if,” but use “if and only if” in the middle of the sentence.
*Since the statements are equivalent, it does not matter which one comes first.

5. Example
Refer to the definition of perpendicular lines and its converse.
The biconditional statement would be:
Two lines are perpendicular if and only if they intersect and form a right angle.
*An equivalent statement would be:
Two lines intersect and form a right angle iff they are perpendicular.

6. True Biconditional Statements
Biconditional statements are true if and only if its conditional statement and its converse are both true. Example: x = 3 iff . If x = 3, then . True or false? If , then x = 3. True or false? *Because the converse is false, the biconditional statement is also false.

7. Can this statement be made into a TRUE biconditional statement?
Example #1 If a number ends in zero, then it is divisible by 5. Converse: If a number is divisible by 5, then it ends in zero. ANSWER: The conditional statement is true, but the converse is false. So the answer is NO.

8. Example #2 If , then x = 2 or –2. Converse: If x = 2 or –2, then
Example #2 If , then x = 2 or –2. Converse: If x = 2 or –2, then . ANSWER: Since both statements are true, this may be written as a true biconditional statement. Biconditional Statement: iff x = 2 or –2.

9. Homework Assignment
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