Logic and Truth

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Logic and Truth
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Proposition

• A declarative sentence that is either true or
  false, but not both.
• Which of the following are propositions?
• Summer session started on May 23.
• The number 13 is prime.
• There is no life on any other planet but Earth.
• It never rains in Illinois.
• Go to the corner and take a right.

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Binary and Unary Operators

• Let p and q be propositions
• Conjunction of p and q (AND)
• Disjunction of p and q (INCLUSIVE OR)
• Negation of p (NOT)

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Truth Tables
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Create a truth table for

• 1.
• 2.
• 3.
• 4.

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Conditional Proposition

• A conditional proposition (statement) or
  implication is denoted p?q.
• Reads if p then q
• p is referred to as the hypothesis or antecedent
• q is referred to as the conclusion or consequent

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Biconditional Proposition

• A biconditional proposition is denoted p?q.
• Reads p if and only if q
• p iff q

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Create a truth table for

• 1.
• 2.
• 3.
• 4.

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Tautology and Logical Equivalence

• A tautology is a statement that is always true
  for all possible values of its propositional
  variables. A contradiction is always false.
• Two statements are said to be logically
  equivalent if they have the same truth values no
  matter what truth values the propositional
  variables constitute (same truth tables p ?q is
  a tautology).
• Equivalence is denoted with

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DeMorgans Laws

• 1.
• 2.

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Show the following equivalences

• 1. Contrapositive
• 2.

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Are the following logically equivalent?

• 1. ??
• 2. ??