1. 2-2: Conditional Statements
Objectives
Identify, write and analyze the truth value of conditional statements.
Write the inverse, converse and contrapositive of a conditional statement.

2. Conditional Statement
Vocabulary
Sketch
Things to remember
2-2
XXXX
NOTATION:
A statement that can be written in if p, then q form.
Conditional Statement
 The “if” or p part of a conditional statement.
Hypothesis
 The “then” or q part of the conditional statement.
Conclusion
NOTATION:  read “not”
The negation of a true statement is false and a false statement is true.
Negation

3. Converse Inverse Contrapositive Vocabulary Sketch Things to remember
2-2
XXXX
NOTATION:
Switch the “if” and “then” parts of conditional statement.
Converse
Negate the “if” and “then” in the conditional statement.
Inverse
Switch and negate the “if” and “then” in the conditional statement.
Contrapositive

4. 2-2: Conditional Statements
If p, then q
Hypothesis: If p
Conclusion: then q p q

5. 2-2: Conditional Statements
If an animal is a Blue
Jay, then it is a bird.
Blue Jays
Birds
Hypothesis:
Conclusion:
If an animal is a Blue Jay
Then it is a bird.

6. 2-2: Conditional Statements
If today is Thanksgiving, then today is Thursday.
Thanksgiving
Thursday
Hypothesis:
Conclusion:
If today is Thanksgiving,
Then today is Thursday.

7. 2-2: Conditional Statements
A number is a rational number if it is an integer.
Rational number
integer
Hypothesis:
Conclusion:
If a number is an integer,
Then it’s a rational number.

8. 2-2: Conditional Statements
Many sentences without the words if and then can be written as conditionals. To do so, identify the sentence’s hypothesis and conclusion by figuring out which part of the statement depends on the other.
Write a conditional statement from:
Two angles that are complementary are acute.
If two angles are complementary, then they are acute.

9. 2-2: Conditional Statements
A conditional statement has a truth value of either true (T) or false (F). It is false only when the hypothesis is true and the conclusion is false.
To show that a conditional statement is false, you need to find only one counterexample where the hypothesis is true and the conclusion is false.
If the hypothesis is false, the conditional statement is true, regardless of the truth value of the conclusion.
Remember!

10. 2-2: Conditional Statements
Determine if the conditional is true. If false, give a counterexample.
If this month is August, the next month is September.
True
If two angles are acute, then they are congruent.
False. Counterexample:________________
If an even number greater than 2 is prime, then = 8.
True. Hypothesis is false.
If a number is odd, then it is divisible 3.
False. Counterexample:_______________________________

11. 2-2: Conditional Statements
The negation of statement p is “not p,” written as ~p. The negation of a true statement is false, and the negation of a false statement is true.

12. 2-2: Conditional Statements
Determine which statement is the converse, inverse and contrapositive of the conditional statement. Use the science fact to find the truth value of each.
Science Fact
Adult insects have six legs.
No other animals have six legs.
If an animal is an adult insect, then it has six legs.
If an animal is not an adult insect, then it doesn’t have six legs.
p q
True
If an animal doesn’t have six legs, then it is not an adult insect.
q p
True
If an animal has six legs,
then it is an adult insect.
q p
True

13. 2-2: Conditional Statements
Determine which statement is the converse, inverse and contrapositive of the conditional statement. Find the truth value of each.
If an animal is a cat, then it has four paws.
If an animal doesn’t have four paws, then it isn’t a cat.
True
q p
If an animal has four paws,
then it is a cat.
q p
False
If an animal is not a cat, then it doesn’t have four paws.
p q
False

14. 2-2: Conditional Statements
Logically Equivalent Statements:
Related conditional statements that have the same truth value.
Conditional Statement  Contrapositive
Inverse  Converse
The logical equivalence of a conditional and its contrapositive is known as the Law of Contrapositive.
Helpful Hint

15. 2-2: Conditional Statements
Assignment
p. 84: 2-36 even