Which of the following relational algebra operations from set theory are commutative?

Question

BlackTom AI · Accepted Answer

When considering which relational algebra operations from set theory are commutative, we examine whether swapping the operands yields the same result for each operation.
Option 1: 'Only Union' asserts that Union is commutative but excludes Intersection. While Union is indeed commutative, Intersection is also commutative, so this option is incomplete and thus incorrect.
Option 2: 'Only Intersection' claims that only Intersection is commutative. Since Union is another commutative operation, this option omits a correct commutative case and is therefore false.
Option 3: 'Only Union and Intersection' states that both Union and Intersection are commutative. This aligns with standard set-theoretic properties where A ∪ B = B ∪ A and A ∩ B = B ∩ A for any relations A and B, making this option consistent with commutativity of both operations.
Option 4: 'Union, Intersection and Difference' suggests that Difference is commutative as well. In fact, set difference is not commutative because A − B is generally not equal to B − A (order matters and can yield different results), so this option is incorrect.
Option 5: 'None are commutative' denies commutativity altogether. Since both Union and Intersection are known to be commutative, this statement is contradicted by fundamental properties and is false.
Thus, the analysis shows that the statements in options 1, 2, 4, and 5 conflict with standard relational-algebra facts about commutativity, while option 3 accurately reflects the commutativity of Union and Intersection.

Which of the following relational algebra operations from set theory are commutative?

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