Matching Set Laws

This question requires matching fundamental Set Laws from List-I with their corresponding mathematical forms in List-II.

Idempotent Law Match

The Idempotent law states that applying an operation to a set with itself results in the same set. For the union operation, this is represented as $A\cup A=A$. This matches form III in List-II.

Commutative Law Match

The Commutative law states that the order of sets does not affect the outcome of the operation. For the union operation, this is $A\cup B=B\cup A$. This matches form I in List-II.

Associative Law Match

The Associative law states that the grouping of sets does not change the outcome when performing the same operation multiple times. For intersection, this is represented as $A\cap (B\cap C)=(A\cap B)\cap C$. This matches form II in List-II.

De-Morgan Law Match

De-Morgan's laws provide rules for negating set operations. One of the laws states that the complement of the intersection of two sets is the union of their complements: $(A\cap B)'=A'\cup B'$. This matches form IV in List-II.

Correct Matching

Based on the analysis:

• A. Idempotent law matches with III. ($A\cup A=A$)
• B. Commutative law matches with I. ($A\cup B=B\cup A$)
• C. Associative law matches with II. ($A\cap (B\cap C)=(A\cap B)\cap C$)
• D. De-Morgan law matches with IV. ($(A\cap B)'=A'\cup B'$)

Therefore, the correct option is A-III, B-I, C-II, D-IV.