Question:
Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of \(A \times B\) having 3 or more elements is :
Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of \(A \times B\) having 3 or more elements is :
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\(A\times B\) has 8 elements; count all subsets and remove those with fewer than 3 elements.
Updated On: Nov 13, 2026
- 219
- 211
- 256
- 220
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The Correct Option is A
Solution and Explanation
\(n(A\times B)=2\times 4=8\).
Total subsets \(=2^8=256\).
Subsets with 0, 1, 2 elements: \(\binom80+\binom81+\binom82=1+8+28=37\).
Required number \(=256-37=219\).
Answer: (1) 219
Total subsets \(=2^8=256\).
Subsets with 0, 1, 2 elements: \(\binom80+\binom81+\binom82=1+8+28=37\).
Required number \(=256-37=219\).
Answer: (1) 219
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