Boolean Identities for OR Operation:
The OR operation in the Boolean algebra is indicated by (+). Following are the Boolean identities for the OR operation.
A + B = B + A (Commutative Law)
This implies that the input A and B of the OR gate may be interchanged without changing the output Y. It may be justified from the truth table of two-input OR gate. For A = B, it is apparent that it doesn't matter when we interchange A and B. When A = 0 and B = 1, if we interchange A and B, then it shall become the case of A = 1 and B = 0 and for both these case the output is 1. Therefore it doesn't matter to the output if we interchange A and B inputs.
A + B + C = (A + B) + C = A + (B + C) (Associative Law)
This means that the order of combining the input variables contain no effect on the output variables. This may be verified from the truth table for three-input OR gate.
A + A = A
This means that any variable ORed with itself equals the variable. We may justify this Boolean identity by substituting the two possible values of A. For A = 0, 0 + 0 = 0 and for A = 1, 1 + 1 = 1 is true (refer to truth table for two-input OR gate).
A + 1 = 1
If one input of the OR gate is high the output is high despite what is the other input. For A = 0, 0 + 1 = 1 and for A = 1, 1 + 1 = 1 is true.
A + 0 = A
This means a Boolean variable ORed with 0 equals the variable. For A = 0, 0 + 0 = 0 and A = 1, 1 + 0 = 1 is true.