Lesson 2-2 Logic. Ohio Content Standards: Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example,

Lesson 2-2Lesson 2-2

LogicLogic

Ohio Content Standards:

Ohio Content Standards:

Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.

Ohio Content Standards:

Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof.

Ohio Content Standards:

Generalize and explain patterns and sequences in order to find the next term and the nth term.

Statement

Statement

Any sentence that is either true or false.

Truth Value

Truth Value

The truth or falsity of a statement.

Negation

NegationHas the opposite

meaning as well as an opposite truth value.

NegationHas the opposite

meaning as well as an opposite truth value.

~p, is read not p

Compound Statement

Compound Statement

When two or more statements are joined.

Conjunction

ConjunctionCompound statement

formed by joining two or more statements with the word and.

ConjunctionCompound statement

formed by joining two or more statements with the word and.

p ^ q reads p and q

Use the following statements to write a compound statement for each conjunction. Then find its

truth value.

Use the following statements to write a compound statement for each conjunction. Then find its

truth value.

p: p: One foot is 14 inches.One foot is 14 inches.

q:q: September has 30 days. September has 30 days.

r:r: A plane is defined by three A plane is defined by three noncollinear points.noncollinear points.

Use the following statements to write a compound statement for each conjunction. Then find its

truth value.

p: p: One foot is 14 inches.One foot is 14 inches.

q:q: September has 30 days. September has 30 days.

r:r: A plane is defined by three A plane is defined by three noncollinear points.noncollinear points.

p p and and qq

Use the following statements to write a compound statement for each conjunction. Then find its

truth value.

p: p: One foot is 14 inches.One foot is 14 inches.

q:q: September has 30 days. September has 30 days.

r:r: A plane is defined by three A plane is defined by three noncollinear points.noncollinear points.

r r ^ pp

Use the following statements to write a compound statement for each conjunction. Then find its

truth value.

p: p: One foot is 14 inches.One foot is 14 inches.

q:q: September has 30 days. September has 30 days.

r:r: A plane is defined by three A plane is defined by three noncollinear points.noncollinear points.

~~q q ^ rr

Use the following statements to write a compound statement for each conjunction. Then find its

truth value.

p: p: One foot is 14 inches.One foot is 14 inches.

q:q: September has 30 days. September has 30 days.

r:r: A plane is defined by three A plane is defined by three noncollinear points.noncollinear points.

~~p p ^ rr

Disjunction

DisjunctionCompound statement

formed by joining two or more statements with the word or.

DisjunctionCompound statement

formed by joining two or more statements with the word or.

p q reads p or q

Use the following statements to write a compound statement for each disjunction. Then find its

truth value.

Use the following statements to write a compound statement for each disjunction. Then find its

truth value.

p: p: AB is proper notation for AB is proper notation for ““line Aline ABB ””..

q:q: Centimeters are metric units. Centimeters are metric units.

r:r: 9 is a prime number. 9 is a prime number.

Use the following statements to write a compound statement for each disjunction. Then find its

truth value.

p: p: AB is proper notation for AB is proper notation for ““line Aline ABB ””..

q:q: Centimeters are metric units. Centimeters are metric units.

r:r: 9 is a prime number. 9 is a prime number.

p p or or qq

Use the following statements to write a compound statement for each disjunction. Then find its

truth value.

p: p: AB is proper notation for AB is proper notation for ““line ABline AB””..

q:q: Centimeters are metric units. Centimeters are metric units.

r:r: 9 is a prime number. 9 is a prime number.

q q rr

The Venn diagram shows the number of students enrolled in Monique’s Dance

School for tap, jazz, and ballet classes.

Tap 28

Jazz43

29Ballet

17 25

13

9

The Venn diagram shows the number of students enrolled in Monique’s Dance

School for tap, jazz, and ballet classes.

• How many students are How many students are enrolled in all three classes?enrolled in all three classes?

Tap 28

Jazz43

29Ballet

17 25

13

9

The Venn diagram shows the number of students enrolled in Monique’s Dance

School for tap, jazz, and ballet classes.

• How many students are How many students are enrolled in tap or ballet?enrolled in tap or ballet?

Tap 28

Jazz43

29Ballet

17 25

13

9

The Venn diagram shows the number of students enrolled in Monique’s Dance

School for tap, jazz, and ballet classes.

• How many students are enrolled How many students are enrolled in jazz and ballet and not tap?in jazz and ballet and not tap?

Tap 28

Jazz43

29Ballet

17 25

13

9

Assignment:

Pgs. 72 - 74 18-28 evens, 56-72 evens