Logic Mathematics question?

(A ^ B ) V ( A -> B )  

Is this valid? 

2 Answers

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  • fcas80
    Lv 7
    2 months ago

    If the truth table has a row where the conclusion column is FALSE while every premise column is TRUE, then the argument is INVALID. Otherwise, the argument is VALID.   This argument is valid.

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  • Sean
    Lv 5
    2 months ago

    This is simply an assertion and as such is valid. What you are trying to determine I suspect is whether the statement is ever true.

    The truth table

    for

    (A ^  B )  V (  A ->  B )     RESULT       A      B

    (T ^ T )  V ( T -> T )          T                  T      T

    (T ^ F )  V ( T -> F )          F                  T      F

    (F ^ T )  V ( F-> T )           T                  F      T

    (F ^ F )  V ( F -> F )          T                  F      F

    (A ^ B )  V ( A -> B )  IS FALSE IF  A IS TRUE AND B IS FALSE AND OTHERWISE TRUE

    TO BREAK IT DOWN TO THE SIMPLEST FORM

    (A -> B) ^(-A v B)

    (A ^ B )  V ( A -> B )  =

    (A^B)  v (-A v B)

    (-AvB) v (A^B)

    (-AvB)vA ^ (-AvB)vB

    (-A v A v B) ^ (-A v B vB)

    (T v B) ^ (-A v B)

    T ^ (-A v B)

    = (-A v B)

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