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Two sets A and B are as under:
$A = {(a, b) ∈ R × R : | a − 5 | < 1, | b − 5 | < 1}$
$B = (a, b) ∈ R × R : 4 (a − 6) 2 + 9 (b − 5) 2 ≤ 36$ , then

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B ⊂ A

A ∩ B = ϕ

(an empty set)

A ⊂ B

neither

A ⊂ B nor B ⊂ A

answer is A.

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Detailed Solution

A = {(a, b) ∈ R × R : | a − 5 | < 1, | b − 5 | < 1}

Let

a − 5 = x, b − 5 = y

Set A contains all points inside

| x | < 1, | y | < 1

B = (a, b) ∈ R × R : 4 (a − 6) 2 + 9 (b − 5) 2 ≤ 36

set B contains all points inside or on

(x − 1) 2 9 + y 2 4 = 1

∴ (± 1, ± 1)

lies inside the ellipse
Hence

A ⊂ B

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