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Simple truth table

  1. Aug 20, 2011 #1
    I need to find the formula involving [itex]\neg[/itex], [itex]\wedge[/itex] or [itex]\vee[/itex] for the following truth table with the variables P and Q:

    P Q formula
    F F F
    F T T
    T F T
    T T F

    The closest I've gotten is something like P[itex]\vee(\neg[/itex]P[itex]\wedge[/itex]Q) which clearly doesn't work for the last row. Any ideas?
     
  2. jcsd
  3. Aug 20, 2011 #2
    That's the truth table for "exclusive or".

    ¬P∧Q is only true with P = F and Q = T. (line 2)

    P∧¬Q is only true with P = T and Q = F. (line 3)

    These are what are known as minterms. Minterms are expressions using only conjunction and negation (∧ and ¬), which are true for the inputs from one line of the truth table with a true output. Each input should be represented in the minterm.

    The disjunction (∨) of all minterms will be an expression that corresponds to the truth table.
     
    Last edited: Aug 20, 2011
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