Which of the following statement represents commutative law?
2013
Which of the following statement represents commutative law?
- A.
(X + Y) + Z = X + (Y + Z)
- B.
X . (Y + Z) = (X . Y) + (X . Z)
- C.
X + Y = Y + X
- D.
X + X = X
Attempted by 57 students.
Show answer & explanation
Correct answer: C
Concept
A commutative law states that the order of the two operands does not change the result of the operation. In Boolean algebra (as in ordinary algebra), an operation is commutative when swapping the two terms on either side of the operator leaves the value unchanged.
Application
Compare each statement against that definition — we need exactly one operator with its two operands swapped and nothing else changed:
X + Y = Y + X : the two operands of the same OR operation are simply interchanged, with no regrouping and no second operator. This matches the commutative law exactly.
Cross-check / Contrast
(X + Y) + Z = X + (Y + Z) : the operands keep their order but the grouping (parentheses) is shifted — this is the associative law, not commutation.
X . (Y + Z) = (X . Y) + (X . Z) : an AND is spread across an OR of two terms — this is the distributive law.
X + X = X : a term combined with itself returns the same term — this is the idempotent law.
Only the statement that interchanges the two operands of a single operation expresses commutativity, so X + Y = Y + X is the commutative law.