Solution

The correct answer is A - III, B - II, C - I, D - IV

Key Points

• A Δ B:
  • This represents the symmetric difference between sets A and B. It includes all those elements which are in A and B but not in their intersection. Mathematically, it can be represented as (A - B) ∪ (B - A). So, A matches with III.
• A - (B ∪ C):
  • This represents all elements in A not in (B or C). Another way to represent it would be (A - B) ∩ (A - C) because it is the intersection of elements that are only in A and not in B or C. So, B matches with II.
• A - (B ∩ C):
  • This represents all elements in A that are not common to both B and C, or equivalently, the elements just in A and not in the intersection of B and C. So, C matches with I.
• A ∩ (B - C):
  • This represents the intersection of A and the elements in B not in C. It is equivalent to (A ∩ B) - (A ∩ C) because you're taking all elements in both A and B, then removing any elements that are also in C. So, D matches with IV.

Therefore, the correct option is A - III, B - II, C - I, D - IV. So, the correct option is 1).