Decide, among the following sets, which sets are subsets of one and another:

Question:

Decide, among the following sets, which sets are subsets of one and another:

$A=\left\{x: x \in R\right.$ and $x$ satisfy $\left.x^{2}-8 x+12=0\right\}$

$B=\{2,4,6\}, C=\{2,4,6,8 \ldots\}, D=\{6\}$

Solution:

$A=\left\{x: x \in R\right.$ and $x$ satisfies $\left.x^{2}-8 x+12=0\right\}$

2 and 6 are the only solutions of $x^{2}-8 x+12=0$

$\therefore A=\{2,6\}$

$B=\{2,4,6\}, C=\{2,4,6,8 \ldots\}, D=\{6\}$

$\therefore D \subset A \subset B \subset C$

Hence, $A \subset B, A \subset C, B \subset C, D \subset A, D \subset B, D \subset C$