Question

Let $A$ and $B$ be two sets of having 3 and 2 elements respectively. Then the number of subsets of $A \times B$ having at least three elements is

• A. 24
• B. 52
• C. 42
• D. 64
• E. 60

Hint:

“At least k elements” = Total subsets - subsets with less than k elements.

Answer 1

The Correct Option is C

Concept: If a set has $n$ elements, number of subsets = $2^n$.

Step 1: Find size of $A \times B$
\[ |A \times B| = 3 \times 2 = 6 \]

Step 2: Total subsets
\[ 2^6 = 64 \]

Step 3: Exclude subsets with < 3 elements}
\[ \binom{6}{0} + \binom{6}{1} + \binom{6}{2} = 1 + 6 + 15 = 22 \]

Step 4: Required subsets
\[ 64 - 22 = 42 \] Final Conclusion:
Option (C)