lesson 2-2 logic. ohio content standards: establish the validity of conjectures about geometric...
TRANSCRIPT
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Lesson 2-2Lesson 2-2
LogicLogic
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Ohio Content Standards:
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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.
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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.
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Ohio Content Standards:
Generalize and explain patterns and sequences in order to find the next term and the nth term.
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Statement
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Statement
Any sentence that is either true or false.
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Truth Value
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Truth Value
The truth or falsity of a statement.
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Negation
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NegationHas the opposite
meaning as well as an opposite truth value.
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NegationHas the opposite
meaning as well as an opposite truth value.
~p, is read not p
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Compound Statement
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Compound Statement
When two or more statements are joined.
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Conjunction
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ConjunctionCompound statement
formed by joining two or more statements with the word and.
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ConjunctionCompound statement
formed by joining two or more statements with the word and.
p ^ q reads p and q
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Use the following statements to write a compound statement for each conjunction. Then find its
truth value.
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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.
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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
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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
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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
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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
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Disjunction
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DisjunctionCompound statement
formed by joining two or more statements with the word or.
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DisjunctionCompound statement
formed by joining two or more statements with the word or.
p q reads p or q
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Use the following statements to write a compound statement for each disjunction. Then find its
truth value.
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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.
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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
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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
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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
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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
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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
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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
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Assignment:
Pgs. 72 - 74 18-28 evens, 56-72 evens