A set A has m elements. Subsets B , C satisfy ∣ B ∣ = ∣ C ∣ , B ∪ C = A , and ∣ B ∩ C ∣ = 1 . Identify the correct statements.

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Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationDistributionHard2 minQB

MathematicsHardmultiple choice

A set $A$ has $m$ elements. Subsets $B, C$ satisfy $∣ B ∣ = ∣ C ∣, B \cup C = A$ , and $∣ B \cap C ∣ = 1$ . Identify the correct statements.

Options:(select one or more)

Answer:

A, C

Solution:

Apart from the one common element, the remaining $m - 1$ elements split equally between $B$ and $C$ , so $m$ is odd. Choose the common element and then the elements exclusive to $B$ : $m (( m - 1 ) /2 m - 1)$ .

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:Distribution

⏱ 2mℹ️ Source: QB

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