Question

Two sets $A$ and $B$ are as under :

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

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

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

Answer 1

The correct option is D

$A\subset B$

The explanation for the correct answer.

Solve for the required value.

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

$$\begin{gathered} -1<a-5<1 \\ 4<a<6 \\ 4<b<6 \end{gathered}$$

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

$4{(a-6)}^2+9{(b-5)}^2\le 36$

$\left(\frac{{\left(a-6\right)}^2}{9}+\frac{{\left(b-5\right)}^2}{4}\right)\le 1$

Hence, option(D) is the correct answer.