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

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Presentation transcript:

Lesson 2-2 Logic

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

Any sentence that is either true or false.

Truth Value

The truth or falsity of a statement.

Negation

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

Negation Has the opposite meaning as well as an opposite truth value. ~p, is read not p

Compound Statement

When two or more statements are joined.

Conjunction

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

Conjunction Compound 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.

p: One foot is 14 inches. q: September has 30 days. r: A plane is defined by three noncollinear points.

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

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 r ^ p

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 ~q ^ r

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 ~p ^ r

Disjunction

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

Disjunction Compound 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.

p: AB is proper notation for “ line AB ”. q: Centimeters are metric units. r: 9 is a prime number.

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

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

The Venn diagram shows the number of students enrolled in Monique ’ s Dance School for tap, jazz, and ballet classes. Tap 28 Jazz Ballet

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?How many students are enrolled in all three classes? Tap 28 Jazz Ballet

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?How many students are enrolled in tap or ballet? Tap 28 Jazz Ballet

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?How many students are enrolled in jazz and ballet and not tap? Tap 28 Jazz Ballet

Assignment: Pgs evens, evens