KCET · Maths · Sets and Relations
If \(A = \{1, 2, 3, 4, \ldots, 10\}\), then the number of non-empty subsets of A containing only even number is
- A \(31\)
- B \(32\)
- C \(30\)
- D \(29\)
Answer & Solution
Correct Answer
(A) \(31\)
Step-by-step Solution
Detailed explanation
Given set \(A = \{1, 2, 3, 4, \ldots, 10\}\).
The subsets must contain only even numbers. The even numbers in set \(A\) are \(2, 4, 6, 8, 10\).
Let \(E\) be the set of even numbers in \(A\), so \(E = \{2, 4, 6, 8, 10\}\).
The number of elements in \(E\) is \(n(E) = 5\).
The total number of subsets of \(E\) is \(2^5 = 32\).
Since we need the number of non-empty subsets, we subtract the empty set.
The number of non-empty subsets of \(E\) is \(2^5 - 1 = 32 - 1 = 31\).
Answer: \(31\)
The subsets must contain only even numbers. The even numbers in set \(A\) are \(2, 4, 6, 8, 10\).
Let \(E\) be the set of even numbers in \(A\), so \(E = \{2, 4, 6, 8, 10\}\).
The number of elements in \(E\) is \(n(E) = 5\).
The total number of subsets of \(E\) is \(2^5 = 32\).
Since we need the number of non-empty subsets, we subtract the empty set.
The number of non-empty subsets of \(E\) is \(2^5 - 1 = 32 - 1 = 31\).
Answer: \(31\)
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