Question

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

• A. $B \subset A$
• B. $A \subset B$
• C. $A \cap B = \phi$ (an empty set)
• D. neither $A \subset B$ nor $B \subset A$

Answer 1

Answer: (B)

$A \subset B$

Answer 2

As, $|a-5|<1$ and $|b-5|<1$ $\Rightarrow 4< a , b <6$ and $\frac{(a-6)^{2}}{9}+\frac{(b-5)^{2}}{4} \leq 1$ Taking axes as $a$-axis and $b$-axis The set $A$ represents square $PQRS$ inside set $B$ representing ellipse and hence $A \subset B$.