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DeMorgans laws and rules of logic

  1. Mar 22, 2009 #1
    1. The problem statement, all variables and given/known data
    (p -> q) has an unambiguous meaning both in logic and in natural language. The DeMorgans laws tell us what is meant by the negation of a conjunction or the negation of a disjunction, but what is the negation of a conditional such as p -> q? Use the rules of logic to produce a meaning for...[not(p -> q), and translate it into natural language using the statement, "If I go to McDonalds, then i will get a Big Mac."


    2. Relevant equations

    ¬ ( p ˅ q ) <=> ( ¬p ˄ ¬ q )
    ¬ ( p ˄ q ) <=> ( ¬p ˅ ¬ q ) De Morgans laws

    3. The attempt at a solution

    ( p  q ) => ( ¬ p ˅ q ) Implication
    ¬ ( p  q ) => ¬ ( ¬ p ˅ q ) Implication
    ¬ ( ¬ p ˅ q ) <=> ( p ˄ ¬ q ) De Morgans
    Translation:
    I went to McDonalds, but I did not get a Big Mac.


    Im not sure if this is the right way to solve this problem does anyone know if this is right or wrong?

    Thanks for your help!
     
  2. jcsd
  3. Mar 22, 2009 #2
    That's right.

    NOT("If I go to McD, then I get a Big Mac")
    <=>
    NOT("I don't go to McD" OR "I get a Big Mac")
    <=>
    NOT("I don't go to McD") AND NOT("I get a Big Mac")
    <=>
    "I go to McD" AND "I don't get a Big Mac"
    <=>
    "I go to McD and I don't get a Big Mac".
     
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