JEE Mains · Maths · STD 11 - 1. set theory
Let \(A :\{1,2,3,4,5,6,7\}\). Define \(B =\{ T \subseteq A\) : either \(1 \notin T\) or \(2 \in T \}\) and \(C = \{ T \subseteq A : T\) the sum of all the elements of \(T\) is a prime number \(\}\). Then the number of elements in the set \(B \cup C\) is \(\dots\dots\)
- A \(107\)
- B \(106\)
- C \(105\)
- D \(108\)
Answer & Solution
Correct Answer
(A) \(107\)
Step-by-step Solution
Detailed explanation
\(B^{\prime}\) is a set containing sub sets of \(A\) containing element \(1\) and not containing \(2\) . And \(C^{\prime}\) is a set containing subsets of \(A\) whose sum of elements is not prime. So, we need to calculate number of subsets of \(\{3,4,5,6,7\}\) whose sum of…
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