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Lesson 2-2. Logic. 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:.

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ohio content standards1
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 standards2
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 standards3
Ohio Content Standards:

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

statement1
Statement

Any sentence that is either true or false.

truth value1
Truth Value

The truth or falsity of a statement.

negation1
Negation

Has the opposite meaning as well as an opposite truth value.

negation2
Negation

Has the opposite meaning as well as an opposite truth value.

~p, is read not p

compound statement1
Compound Statement

When two or more statements are joined.

conjunction1
Conjunction

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

conjunction2
Conjunction

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

p^ q reads p and q

slide18
Use the following statements to write a compound statement for each conjunction. Then find its truth value.
slide19
Use the following statements to write a compound statement for each conjunction. Then find its truth value.

p: One foot is 14 inches.

q: September has 30 days.

r: A plane is defined by three noncollinear points.

slide20
Use the following statements to write a compound statement for each conjunction. Then find its truth value.

p: One foot is 14 inches.

q: September has 30 days.

r: A plane is defined by three noncollinear points.

p and q

slide21
Use the following statements to write a compound statement for each conjunction. Then find its truth value.

p: One foot is 14 inches.

q: September has 30 days.

r: A plane is defined by three noncollinear points.

r ^p

slide22
Use the following statements to write a compound statement for each conjunction. Then find its truth value.

p: One foot is 14 inches.

q: September has 30 days.

r: A plane is defined by three noncollinear points.

~q ^r

slide23
Use the following statements to write a compound statement for each conjunction. Then find its truth value.

p: One foot is 14 inches.

q: September has 30 days.

r: A plane is defined by three noncollinear points.

~p ^r

disjunction1
Disjunction

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

disjunction2
Disjunction

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

pq reads p or q

slide27
Use the following statements to write a compound statement for each disjunction. Then find its truth value.
slide28
Use the following statements to write a compound statement for each disjunction. Then find its truth value.

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

q: Centimeters are metric units.

r: 9 is a prime number.

slide29
Use the following statements to write a compound statement for each disjunction. Then find its truth value.

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

q: Centimeters are metric units.

r: 9 is a prime number.

p or q

slide30
Use the following statements to write a compound statement for each disjunction. Then find its truth value.

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

q: Centimeters are metric units.

r: 9 is a prime number.

q r

slide31
The Venn diagram shows the number of students enrolled in Monique’s Dance School for tap, jazz, and ballet classes.

Tap

28

Jazz

43

13

9

17

25

29

Ballet

slide32
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 in all three classes?

Tap

28

Jazz

43

13

9

17

25

29

Ballet

slide33
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 in tap or ballet?

Tap

28

Jazz

43

13

9

17

25

29

Ballet

slide34
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 in jazz and ballet and not tap?

Tap

28

Jazz

43

13

9

17

25

29

Ballet