2-2: Conditional Statements
Conditional Statements
1.
Conditional
◦


Parts of a Conditional
1. Hypothesis

If-then statement
Symbols
◦ pq
◦ Read as
“If p then q” or
“p implies q”
◦
2.
The part p following if
Conclusion
◦
The part q following
then
Diagram
q
p
1
Identifying the Hypothesis and Conclusion
If a number is even,
even then it is divisible by 2.
2
Hypothesis (p): a number is even
Conclusion (q): it is divisible by 2
Complete Got It? #1 p.90
Hypothesis: An angle measures 130
Conclusion: The angle is obtuse
Writing a Conditional
Adjacent angles share a side
side.
Step 1:
Identify the hypothesis and conclusion
Step 2:
Write the conditional:
If two angles are adjacent, then they share a side.
Complete Got It? #2 p.90
If an animal is a dolphin, then it is a mammal.
Finding Truth Values of Conditionals

Truth Value
◦ Conditional is true if both hypothesis and conclusion
are true.
◦ Conditional is false if the hypothesis is true but the
conclusion is proved false.
Is the conditional true or false? If false, give a counterexample
______________
1) If you live in Miami, then you live in Florida..
True
2) If a number is divisible by 5, then it is odd.
False. Counterexample: 10 is divisible by 5 but is not odd.
Complete Got It? #3 p. 90 a. False, Every month has 28 days
b. True
2
Negation
~
• Opposite of the statement
If mA  15
If mA  15
Conditional
→
If mA  15, then A is acute.
1. Converse
→
◦ Switch the hypothesis and conclusion
If A is acute, then mA  15.
2. Inverse
~ →~
◦ Negate both hypothesis and conclusion of conditional.
If mA  15, then A is not acute.
3. Contrapositive
~ →~
◦ Negate both hypothesis and conclusion of converse.
If A is not acute, then mA  15.
Equivalent Statements

Statements that have the same truth value.
Statement
Example
Truth Value
Conditional
If mA  15, then A is acute .
True
Converse
If A is acute, then mA  15.
False
Inverse
If mA  15, then A is not acute.
False
Contrapositive
If A is not acute, then mA  15.
True
3
What are the converse, inverse and contrapositive of
the conditional below. If a statement is false, give a
counterexample.
If a figure is a rectangle, then it is a parallelogram.

Converse:
If a figure is a parallelogram, then it is a rectangle.

Inverse:
If a figure is not a rectangle, then it is not a parallelogram.

Contrapositive:
If a figure is not a parallelogram, then it is not a
rectangle.

Counterexample: For the Converse
If a figure is a parallelogram with angles not equal to 90˚
Homework: p. 93 #5-11odd, 17-31 odd, 47-58
Read p. 57-58 and define highlighted words
4