Geometry: Logic

Truth Tables!

Do Now:

• What is the converse, inverse, and contrapositive of the following conditional statement.

If I am sleepy, then I will yawn a lot.

Truth Tables

• A statement is a sentence that is either true or false. – These statements are like the parts of conditional

statements we looked at yesterday (i.e. p/q)

• The truth value of a statement is either true (T) or False (F).

True or False?

• A rectangle is a quadrilateral

• It is raining outside

• Supplementary Angles add to 90 degrees.

Compound Statement

• Two or more statements joined by the word and or or.

– So Two Types! AND or OR

Conjunction

A Conjunction is a compound statement with and

Symbol: p^q

Ex: Ms. Stonebraker teaches geometry and algebra.

Example

• Use the following statements to write a compound statement for each conjunction. Then find the truth value.

p: The figure is a triangleq: The figure has two congruent sidesr: The figure has three acute angles

So….. p^r =

So… q^

Truth Tables

• A convenient method for organizing truth values of statements.

Truth Value for Conjunctionp q p^q

T T

T F

F T

F F

Disjunction

• A compound statement that uses the word or

Ex: Billy studies geometry or chemistry.

Symbol: p V q

Example• Use the following statements to write a compound statement for

each disjunction. Then find its truth value.

p: January is a fall monthq: January has only 30 daysr: January 1 is the first day of a new year.

pVr

pVq

Truth Value for Disjunctionp q pVq

T T

T F

F T

F F

Venn Diagram

• A disjunction/conjunction can also be illustrated with a Venn Diagram! Think about it.

Example

• The Venn Diagram shows the number of people who can or cannot attend the May or the June Spanish Club meetings.

5 146

MAY June

Example Two

• The Venn Diagram shows the number of graduates last year who did or did not attend their junior or senior prom.

85 25Junior

123

Senior

37

Practice

• Try some on your own! • As always if you are confused please call me

over!

Exit Ticket

• The Venn Diagram shows the students who take geometry and statistics. How many students took geometry or statistics? How many took geometry and statistics? What does the 25 represent?

60 40Geometry

5

Statistics

25