Biconditional: Points lie on the same line if and
only if they are collinear.

For a biconditional statement to be true,
both the conditional statement and its
converse must be true. If either the
conditional or the converse is false, then
the biconditional statement is false.

Determine if the biconditional is true. If false,
give a counterexample.
Example 3A: Analyzing the Truth Value of a Biconditional
Statement
A rectangle has side lengths of 12 cm and 25 cm
if and only if its area is 300 cm
2
.

Check It Out!
Example 3a
An angle is a right angle iff its measure is 90°.
Determine if the biconditional is true. If false,
give a counterexample.

Lesson Quiz: Part I
Identify the hypothesis and conclusion of each
conditional.
1.
A triangle with one right angle is a right triangle.
2.
All even numbers are divisible by 2.
3.
Determine if the statement “If
n
2
= 144, then
n
= 12” is true. If false, give a counterexample.

Lesson Quiz: Part II
Identify the hypothesis and conclusion of
each conditional.
4.
Write the converse, inverse, and contrapositive
of the conditional statement “If Maria’s birthday is
February 29, then she was born in a leap year.”
Find the truth value of each.

p
q
p → q
T
T
T
T
F
F
F
T
T
F
F
T
So p → q follows the following reasoning:
•
a True premise implies a True conclusion, therefore T → T is T;
•
a True premise cannot imply a False conclusion, therefore T → F is F; and
•
you can conclude anything from a false assumption, so F → anything is T.

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- Summer '18
- Jane Smith
- Logic