Question

Let 'U' be universal set. If A and B are subsets of U, then match the following and choose the correct answer.

• A. a - ii, b - i, c - iv, d - iii
• B. a - ii, b - iii, c - iv, d - i
• C. a - iii, b - iv, c - ii, d - i
• D. a - iv, b - iii, c - ii, d - i

Hint:

De Morgan’s Laws are easiest to remember as: “Break the line, change the sign” - Union becomes intersection - Intersection becomes union while keeping complements on each term.

Answer 1

The Correct Option is D

Step 1: Evaluate (a) \(A \cup A'\) Every element in the universal set either belongs to \(A\) or does not belong to \(A\). Hence their union covers the entire universal set: \[ A \cup A' = U \] So, (a) matches with (iv).

Step 2: Evaluate (b) \((A \cup B)'\) Using De Morgan’s law, the complement of union becomes intersection of complements: \[ (A \cup B)' = A' \cap B' \] So, (b) matches with (ii).

Step 3: Evaluate (c) \((A \cap B)'\) Using De Morgan’s law again, the complement of intersection becomes union of complements: \[ (A \cap B)' = A' \cup B' \] So, (c) matches with (iii).

Step 4: Evaluate (d) \((A')'\) Applying double complement law: \[ (A')' = A \] So, (d) matches with (i). Final Matching: \[ a \rightarrow (iv), \quad b \rightarrow (ii), \quad c \rightarrow (iii), \quad d \rightarrow (i) \] Thus, the correct option is: \[ {(D)} \]