1. Warmup State whether each sentence is true or false.
If you live in Los Angeles, then you live in California.
If you live in California, then you live in Los Angeles.
If today is Wednesday, then tomorrow is Thursday.
If tomorrow is Thursday, then today is Wednesday.
True
False
True
True

2. 2.1 Conditional Statements

3. Conditional Statement
Conditional statement has two parts, hypothesis and a conclusion.
If _____________, then____________.
Words Symbols
If p, then q. p q
hypothesis
conclusion

4. Example 1 Write as a conditional
a) A number divisible by 9 is also divisible by 3.
If a number is divisible by 9, then it is divisible by 3.
b) Two points are collinear if they lie on the same line.
If two points lie on the same line, then they are collinear.

5. Counterexample
Write a counterexample to show that the following conditional statement is false.
If x2 = 16, then x = 4.
Counterexample: x = -4

6. Negation writing the negative of the statement. Words Symbols not p ~p
Examples:
Statement: m < A = 30°
Negation: m < A ≠ 30°
Statement: The cat is black.
Negation: The cat is not black.

7. Converse
To write the converse of a conditional, switch the hypothesis and conclusion.
Words Symbols
If q, then p. q p
If two points are collinear, then they lie on the same line.
If two points lie on the same line, then they are collinear.
Conditional Statement
Converse

8. Inverse
To write the inverse of the conditional statement, negate both hypothesis and conclusions
Words Symbols
If not p, then not q ~p ~q
If two points are collinear, then they lie on the same line.
If two points are not collinear, then they do not lie on the same line.
Conditional
Inverse

9. Contrapositive
To write a contrapositive of conditional, first write the converse, then negate both hypothesis and conclusion.
Words Symbols
If not q, then not p. ~q ~p
If two points lie on the same line, then they are collinear.
If two points are not collinear, then they do not lie on the same line.
Conditional
Contrapositive

10. Equivalent Statements
When two statements are both true or both false, they are called equivalent statements.
A conditional statement is equivalent to its contrapositive.
The inverse and converse of any conditional statement are equivalent.

11. Decide if the statement is true or false.
Example 2
Write the:
a) conditional
b) converse
c) inverse
d) contrapositive
Decide if the statement is true or false.

12. Let p be “you are a guitar player” and let q be “you are a musician.”
If you are a guitar player, then you are a musician.
If you are a musician, then you are a guitar player.
If you are not a guitar player, then you are not a musician.
If you are not a musician, then you are not a guitar player.
True
False
False
True

13. You try! Let p be “the stars are visible” and let q be “it is night”
a) If the stars are visible, then it is night.
true
b) If it is night, then the stars are visible.
false
c) If the stars are not visible, then it is not night.
d) If it is not night, then the stars are not visible.