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 triangle q: The figure has two congruent sides r: The figure has three acute angles So….. p^r = So… q^ ~𝑟

Truth Tables • A convenient method for organizing truth values of statements.

Truth Value for Conjunction

p^q

F F

p

T T T F

q

T 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 month q: January has only 30 days r: January 1 is the first day of a new year.

pVr pVq

~𝑝 𝑉 𝑟

Truth Value for Disjunction

pVq p

T T F F

q

T F T 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. MAY 5 6 June 14

Example Two

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

Junior

85

123 Senior

25

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?

Geometry

60

5 Statistics

40

25