If n ( A ) = 1000 , n ( B ) = 500 and if n ( A ∩ B ) ≥ 1 and n ( A ∪ B ) = p , then

n ( A ) = 1000 , n ( B ) = 500 , n ( A ∩ B ) ≥ 1 , n ( A ∪ B ) = p ; n ( A ∪ B ) = n ( A ) + n ( B ) − n ( A ∩ B ) p = 1000 + 500 − n ( A ∩ B ) ⇒ 1 ≤ n ( A ∩ B ) ≤ 500 Hence p ≤ 1499 and p ≥ 1000 ⇒ 1000 ≤ p ≤ 1499

Mathematics - Sets and Relations Question with Solution | TestHub

MathematicsSets and RelationsQuestions on number of relations and setsEasy2 minPYQ_2023

MathematicsEasysingle choice

If $n (A) = 1000, n (B) = 500$ and if $n (A \cap B) \geq 1$ and $n (A \cup B) = p$ , then

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Answer:

Solution:

$n (A) = 1000, n (B) = 500, n (A \cap B) \geq 1$ , $n (A \cup B) = p; n (A \cup B) = n (A) + n (B) - n (A \cap B)$ $p = 1000 + 500 - n (A \cap B) \Rightarrow 1 \leq n (A \cap B) \leq 500$
Hence $p \leq 1499$ and $p \geq 1000 \Rightarrow 1000 \leq p \leq 1499$

Stream:BITSATSubject:MathematicsTopic:Sets and RelationsSubtopic:Questions on number of relations and sets

⏱ 2mℹ️ Source: PYQ_2023

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