Geometry Notes

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Geometry Notes

• Section 2-2
• 9/21/07

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What youll learn

• How to determine truth values of conjunctions and
  disjunctions
• How to construct truth tables

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Vocabulary

• Statement
• Premise
• Truth value
• negation
• Compound statement
• Conjunction
• Disjunction
• Truth table

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Determining Truth Values

• Statementany sentence that is true or false
• Usually denoted by p or q (the letter p or the
  letter q represents the whole statement)
• Premise just a simple statement
• Truth ValueTwo choices TRUE or FALSE

• Examples
• The carpet is red.
• Today is not Friday.
• All linear pairs of angles are supplementary.

FALSE
FALSE
TRUE
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Negations

• Negation-the opposite of a statement
• Notation-- p

• Go back to the Examples
• The carpet is red.

FALSE

• Negation
• The carpet is not red.

TRUE

• Today is not Friday.
• Negation
• Today is Friday.

FALSE
TRUE
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Determining Truth Values

• One more example . . . .

• All linear pairs of angles are supplementary.

• Negation All linear pairs of angles are not
  supplementary.

TRUE
FALSE

• So if the original statement or premise is TRUE
  the negation will be ________.

• So if the original statement or premise is FALSE
  the negation will be ________.

FALSE
TRUE
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Conjunctions

• A compound statement formed by joining two or
  more simple statements with the word AND.
• Symbolically
• Let p represent a simple statement
• Let q represent a second simple statement
• The conjunction is written as p ? q
• Read as p and q

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Example

• Let p represent It is Friday.
• Let q represent There is no school tomorrow.
• The conjunction is
• It is Friday and there is no school tomorrow.

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Truth Value of Conjunctions-- A conjunction is
only true when both simple statements are true.

• Let p represent It is Friday.
• True or False?
• Let q represent There is no school tomorrow.
• True or False?

TRUE

• Therefore the conjunction
• It is Friday and there is no school
  
• tomorrow.
• is _____________

TRUE
TRUE
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disjunctions

• A compound statement formed by joining two or
  more simple statements with the word OR.
• Symbolically
• Let p represent a simple statement
• Let q represent a second simple statement
• The disjunction is written as p ? q
• Read as p or q

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Example

• Let p represent It is Friday.
• Let r represent It is snowing.
• The disjunction is
• It is Friday or it is snowing.

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Truth Value of Disjunctions-- A disjunction is
true when only one simple statement is true.

• Let p represent It is Friday.
• True or False?
• Let r represent It is snowing.
• True or False?

TRUE
False

• Therefore the disjunction
• It is Friday or it is snowing.
• is _____________

TRUE
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Conjunctions and Disjunctions can be illustrated
by. . . .

• Venn Diagrams

• The overlap is the conjunction p and q.
• The entire shaded area is p or q.

p
q
p?q
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Conjunctions and Disjunctions can be illustrated
by. . . .

• Truth Tables
• You can compute the truth value of a conjunction
  or disjunction using truth tables.
• First consider all possible truth value
  combinations for p and q (You will want to set
  this up the same way each time).

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p?q (BOTH MUST BE TRUE)

• Take it one row at a time

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p ? q
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Have you learned?

• How to determine truth values of conjunctions and
  disjunctions?
• How to construct truth tables?
• Assignment P. 72 (19-73odd) Notes 2-3