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Math Help - Truth Table for discrete math logic

  1. #1
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    Truth Table for discrete math logic

    mn
    Last edited by chillerbros17; February 28th 2007 at 02:39 PM.
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  2. #2
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    Hello, chillerbros17!

    The exclusive-or operation is defined by the following truth table:
    Code:
     p  q | p v q 
    ------+------- 
     T  T |   F 
     T  F |   T 
     F  T |   T
     F  F |   F
    Exclusive-or means "p or q but not both".


    a. Express p v q in terms of p, q, v, ^, ~
    I would write: .(p ^ ~q) v (~p ^ q)


    b. Express p v q in terms of p, q, ^, ~, v
    Tricky . . . the "or" is not in the list.

    So I can't write: .p v q

    But I can use DeMorgan's Law to write: .~(~p ^ ~q)

    . . (This works: It says "It is not true that both are false".)



    c. Show that one of the distributive laws no longer holds when v is replaced by v.
    Compare: . p v (q ^ r) .and ,(p v q) ^ (p v r)
    Code:
     p v (q ^ r)      (p v Q) ^ (P v R)
    ------------      -----------------
     T F  T T T        T F T  F  T F T
     T T  T F F        T F T  F  T T F
     T T  F F T        T T F  F  T F T
     T T  F F F        T T F  T  T T F
     F T  T T T        F T T  T  F T T
     F F  T F F        F T T  F  F F F
     F F  F F T        F F F  F  F T T
     F F  F F F        F F F  F  F F F
             not equal       
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