Two sets A and B are as under A=(a,b)∈R×R:|a−5|

A ∩ B = ∅ ( a n e m p t y s e t )

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Two sets A and B are as under $A = \{(a, b) \in R \times R : | a - 5 | < 1 a n d | b - 5 | < 1\}$ ; $B = \{(a, b) \in R \times R : 4 {(a - 6)}^{2} + 9 {(b - 5)}^{2} \leq 36\}$ . Then

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neither $A \subset B$ nor $B \subset A$

$A \cap B = \emptyset (a n e m p t y s e t)$

$B \subset A$

$A \subset B$

answer is A.

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$A = {(a, b) \in R \times R : | a - 5 | < 1, | b - 5 | < 1}$

Let $a - 5 = x, b - 5 = y$

Set A contains all points inside $| x | < 1, | y | < 1$

$B = \{(a, b) \in R \times R : 4 {(a - 6)}^{2} + 9 {(b - 5)}^{2} \leq 36\}$

Set B contains all points inside or on $\frac{{(x - 1)}^{2}}{9} + \frac{y^{2}}{4} = 1$

$(\pm 1, \pm 1)$ lies inside the ellipse $\Rightarrow A \subset B$

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