KCET · Maths · Sets and Relations
If \(A = \{a, b, c, d, e, f\}\), then the number of subsets of A which contains at least \(2\) elements is
- A \(64\)
- B \(65\)
- C \(57\)
- D \(59\)
Answer & Solution
Correct Answer
(C) \(57\)
Step-by-step Solution
Detailed explanation
Total number of elements in set \(A\) is \(n = 6\).
Total number of subsets of \(A\) is \(2^6 = 64\).
Number of subsets containing \(0\) elements is \(^{6}C_{0} = 1\).
Number of subsets containing \(1\) element is \(^{6}C_{1} = 6\).
Number of subsets containing at least \(2\) elements is equal to the total number of subsets minus the number of subsets with \(0\) or \(1\) element.
Required number of subsets \(= 64 - (1 + 6) = 57\).
Answer: \(57\)
Total number of subsets of \(A\) is \(2^6 = 64\).
Number of subsets containing \(0\) elements is \(^{6}C_{0} = 1\).
Number of subsets containing \(1\) element is \(^{6}C_{1} = 6\).
Number of subsets containing at least \(2\) elements is equal to the total number of subsets minus the number of subsets with \(0\) or \(1\) element.
Required number of subsets \(= 64 - (1 + 6) = 57\).
Answer: \(57\)
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