COMEDK · Maths · 20. Sets and Relations
Two finite sets have \(m\) and \(n\) elements. The total number of proper subsets of the first set is 119 more than the total number of subsets of the second set. Find the value of \(m-n\)
- A \(8\)
- B \(1\)
- C \(6\)
- D \(4\)
Answer & Solution
Correct Answer
(D) \(4\)
Step-by-step Solution
Detailed explanation
The number of subsets of a set with \(m\) elements is \(2^m\). The number of proper subsets of the first set is \(2^m - 1\). The number of subsets of the second set is \(2^n\). According to the problem, \(2^m - 1 = 2^n + 119\). Rearranging the equation, we get…
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