Equivalent Statements

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• Questions?
• Logical Equivalence
  • Section 2.2
  • Examples / problems
    • Which of the following are logically equivalent?
      • Equivalent means results of expressions are the same for all values of input variables
      • Prove equivalence using truth tables or Boolean algebra
      • The statements:
        • P ∧ (Q ∨ ¬R)
        • P ∨ (Q ∧ R)
        • ¬ ( P → ( ¬Q ∧ R) )
      • Spreadsheets are convenient tools for both organizing tabular material and doing calculations
      • This spreadsheet contains a combined truth table for all 3 expressions above
        • Since Excel has and, or, and not logical functions, but not an “implies” one, it was convenient in making this spreadsheet to know the equivalence A → B ≡ ¬A ∨ B
    • Give the converse, contrapositive, and negation of “if Math 239 has English 142 as a prerequisite, then Prof. Baldwin is an aardvark”
      • Converse: “if Prof. Baldwin is an aardvark then Math 239 has English 142 as a prerequisite”
        • Converse of P → Q is Q → P
        • Not equivalent to original implication
      • Contrapositive: “if Prof. Baldwin is not an aardvark then Math 239 does not have English 142 as a prerequisite”
        • Contrapositive of P → Q is ¬Q → ¬P
        • Equivalent to original implication
      • Negation: “Math 239 has English 142 as a prereq and Prof. Baldwin is not an aardvark”
        • Negation of P → Q is P ∧ ¬Q
• Next
  • Proving equivalence via Boolean algebra
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