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Consider two sets A and B such that $A ∪ (B ∩ {1, 2, 3}) = {2, 3, 4, 5}$ , then which of the following is correct?

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1 ∈ A ∪ B

minimum value of n(B) is 2

Minimum value of n(A) is 4

1 ∈ A' ∩ B'

answer is B.

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Detailed Solution

Use properties.

∵ 1 ∉ A ∪ (B ∩ {1, 2, 3})

⇒ 1 ∉ A and 1 ∉ B ∩ {1, 2, 3} ⇒ 1 ∉ A and 1 ∉ B ⇒ 1 ∉ A ∪ B ∵ 4 ∉ B ∩ {1, 2, 3} and 5 ∉ B ∩ {1, 2, 3}

So, the smallest possible set

A = {4, 5}

Also, smallest possible set

B = ϕ (when A = {2, 3, 4, 5})

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