Symbolic Logic

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Symbolic Logic
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Objectives

• Determine if a sentence or question is a
  statement or not.
• Write a sentence that represents the negation of
  a given statement.
• Rewrite a statement in symbolic form (defining
  the symbols used).
• Rewrite a symbolic statement in word form.

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Vocabulary

• Statement
• Compound statement
• Negation
• Conjunction
• Disjunction (inclusive or)
• Conditional (implication)
• Hypothesis (premise)
• Conclusion

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• Statement
• Compound statement

a statement is a sentence that is either true or
false
a statement that contains one or more simpler
statement (not, and, or, if . . . then, only if,
if and only if)
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Determine which of the following are statements.
2. Solve the equation 2x 5 3.
3. x2 1 0 has no solution.
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Connectives

• Negation
• Conjunction
• Disjunction
• Conditional

denial of a statement (symbol )
and (symbol )
or inclusive or (symbol V)
if . . ., then (symbol ?)
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Write the statement that represents the negation

1. His car is not new.
2. Some buildings are earthquakeproof.
3. All children eat candy.
4. I never cry in a movie theater.

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Negation Summary
Statement Negation
Some p are q. No p are q.
All p are q. Some p are not q.
No p are q. Some p are q.
Some p are not q. All p are q.
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Using the symbolic representations p The car
costs 40,000. q The car goes 140 miles per
hour. r The car is red.express the
following compound statements in symbolic form.

1. The car is red, goes 140 mph, and does not cost
   40,000.

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Using the symbolic representations p The car
costs 40,000. q The car goes 140 miles per
hour. r The car is red.express the
following compound statements in symbolic form.

1. If the car does not cost 40,000, it does not go
   140 mph.

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Using the symbolic representations p The car
costs 40,000. q The car goes 140 miles per
hour. r The car is red.express the
following compound statements in symbolic form.

1. The car is red and it does not go 140 mps or cost
   40,000.

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Using the symbolic representations p The car
costs 40,000. q The car goes 140 miles per
hour. r The car is red.express the
following compound statements in symbolic form.

1. All red cars go 140 mph.

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Using the symbolic representations p I am an
environmentalist. q I recycle my aluminum
cans. r I recycle my newspapers.express the
following compound statements in symbolic form.
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Using the symbolic representations p I am an
environmentalist. q I recycle my aluminum
cans. r I recycle my newspapers.express the
following compound statements in symbolic form.
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Using the symbolic representations p I am an
environmentalist. q I recycle my aluminum
cans. r I recycle my newspapers.express the
following compound statements in symbolic form.
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Using the symbolic representations p I am an
environmentalist. q I recycle my aluminum
cans. r I recycle my newspapers.express the
following compound statements in symbolic form.