Associative Laws
Example2: x=0; y=0; z=1
(x V y) V z = x V ( y V z )
(0 V 0) V 1 = 0 V (0 V 1)
(0) V 1= 0 V ( 1)
1 = 1a
Example3: x=0; y=0; z=1
(x ^ y) ^ z = x ^ ( y ^ z )
(0 ^ 0) ^ 1 = 0 ^ (0 ^ 1)
(0) ^ 1 = 0 ^ ( 1)
0 = 0a
Example4: x=0; y=1; z=1
(x ^ y) ^ z = x ^ ( y ^ z )
(0 ^ 1) ^ 1 = 0 ^ (1 ^ 1)
(0) ^ 1 = 0 ^ ( 1)
0 = 0a
It doesn't really matter where the parenthesis are when the binary operations are the same. The reason is if you are using the AND (^) operator, then you need all of the numbers to be equal to 1 if you want to get a solution of 1. In the case of the OR (V) operator, you need to have all the numbers equal to zero if you want to get an output of zero.
Example1: x=0; y=1; z=0
(x V y) V z = x V ( y V z )
(0 V 1) V 0 = 0 V (1 V 0)
(1) V 0 = 0 V ( 1)
1 = 1a
