# Logic Mathematics question?

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

Is this valid?

Relevance
• 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. • 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)