Boolean Functions-Algebraic rules for Boolean functions-Associative Rule

Question

Is the function $(p \wedge q) \vee r$ equal to the function $p \wedge (q \vee r)$?
Let $a(p,q,r)=(p \wedge q) \vee r$
$b(p,q,r)= p \wedge (q \vee r)$
By associate law $a=b$, but using $a(0,0,1)=1$ and $b(0,0,1)=0$?
Any suggestions?

Answer 1

The way the question is written it is not entirely clear what you are asking. You are asked whether two boolean expressions are equal. It seems that you are trying to use associativity somewhere, but it is not clear how (or why). The associative law absolutely does not say that $a=b$. I think that you are also trying to say that $a$ evaluated at $(0,0,1)$ is different than $b$ evaluation at the same values. That is reason enough to conclude the two expressions are different as functions.