True Output

How do you use truth tables to establish the Associative Law?

How do you use truth tables to establish the Associative Law: (P V Q) V R ≡ P V (Q V R)

Public Comments

1. Since we're working with 3 variables, all you have to do is create 2^3 rows, or 8 rows. Write each expression of either side of the biconditional "if and only if", and see if they're always equal to each other. P Q R [ (P V Q) V R ] [ P V (Q V R) ] T T T . . . . . . .T . . . . . . . . . . T T T F . . . . . . .T . . . . . . . . . . T T F T . . . . . . .T . . . . . . . . . . T T F F . . . . . . .T . . . . . . . . . . T F T T . . . . . . .T . . . . . . . . . . T F T F . . . . . . .T . . . . . . . . . . T F F T . . . . . . .T . . . . . . . . . . T F F F . . . . . . .F . . . . . . . . . . F As you can see, they imply each other in every case, verifying the Associative Law holds true.
2. http://users.senet.com.au/~dwsmith/boolean.htm Please give me best answer thanks!