Assertion - nU-600-nA-450-nB-250 nA - B-50 then given data is correct- Reason- nA - B - nU

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Assertion : ...

Question

Assertion : $n (U) = 600, n (A) = 450, n (B) = 250$ & $n (A \cap B) = 50$ then given data is correct. Reason: $n (A \cup B) \leq n (U)$

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is D Assertion is incorrect but Reason is correct
Given $n (U) = 600, n (A) = 450, n (B) = 250$ and $n (A \cap B) = 50$
Now $n (A \cup B) = n (A) + n (B) - n (A \cap B)$
$= 450 + 250 - 50$
$∴ n (A \cup B) = 700 - 50 = 650$
$≮ n (U)$
$∴$ Data is incorrect
$∴$ Asseration (A) is false and the fact $n (A \cup B) \leq n (U)$ is true

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Assertion :n(U)=600,n(A)=450,n(B)=250 & n(A∩B)=50 then given data is correct. Reason: n(A∪B)≤n(U)

The correct option is D Assertion is incorrect but Reason is correctGiven n(U)=600,n(A)=450,n(B)=250 and n(A∩B)=50Now n(A∪B)=n(A)+n(B)−n(A∩B)=450+250−50∴n(A∪B)=700−50=650≮n(U)∴ Data is incorrect∴ Asseration (A) is false and the fact n(A∪B)≤n(U) is true

Assertion : $n (U) = 600, n (A) = 450, n (B) = 250$ & $n (A \cap B) = 50$ then given data is correct. Reason: $n (A \cup B) \leq n (U)$