WARM UP MARCH 12, 2014

1. What is the length of AB2. What is length of CD

ED

C

B

A

10

G

F

8

8

4

D, E, and F are midpoints.

EOCT Week 9 #3

CONDITIONAL STATEMENTS

Also known as logic statements.

Types: Conditional, Inverse, Converse, & Contrapositive

a. Conditional Statements

• Called if-then statements• Have 2 parts• Hypothesis- The part after if.• Conclusion- The part after then.

* Do not include if and then in the hypothesis and conclusion.

Hypothesis and Conclusion

•Example: If you are not satisfied for any reason, then return everything within 14 days for a full refund.

Examples: Identify the Hypothesis and the conclusion.

1. If it is Saturday, then Beckham plays soccer.• Hypothesis-• Conclusion-

2. If points are collinear, then they lie on the same line.

• Hypothesis-• Conclusion-

it is Saturday Beckham plays soccer

points are collinear they lie on the same line

A statement can be altered by negation by writing the negative of the statementSymbol: ~

Negation

When you negate the hypothesis and conclusion of a conditional statement,

you form the inverse.

b. Inverse

Inverse• The inverse of a conditional statement is formed by

negating both the hypothesis and the conclusion in the conditional

(Add “NOT”)

Conditional- If a figure is a triangle, then it has three angles.

• Inverse- If a figure is not a triangle, then it does not have three angles.

c. Converse

• The converse of a conditional statement swaps the hypothesis and the conclusion.

• Conditional- If a figure is a triangle, then it has three angles.

• Converse- If a figure has three angles, then it is a triangle.

* Converses are not always true.• Conditional- If a figure is a square, then it has four

sides.• Converse- If a figure has four sides, then it is a

square.

* Not all four sided figures are squares. Rectangles also have four sides.

CounterexampleGiving at least 1 example that disproves the statement.• Example: All prime numbers are odd.

Contrapositive• The contrapositive of a conditional statement is formed

by switching and negating both the hypothesis and the conclusion.

(SWITCH the order and NEGATE)

• Conditional- If a figure is a triangle, then it has three angles.

• Contrapositive- If it does not have three angles, then a figure is not a triangle.

Recap

Conditional: p → q

Inverse: ~p → ~ q

Converse: q → p

Contrapositive: ~ q → ~ p

Truth ValueDecide whether the statement is true or false. If false, give a counterexample as to why it’s false.STMT: If you are a basketball player, then you are an athlete.Converse:

Inverse:

Contrapositive:

False, not all athletes play basketball. Could play baseball, golf, tennis, swim, etc.

False, even if you don’t play basketball, you can still be an athlete. Again, could play baseball, golf, tennis, swim, etc.

True

Give me some statements!!