Decide, among the following sets, which sets are subsets of one and another:
$A = {x : x ϵ R and x satisfy x^{2} - 8 x + 12 = 0},$
$B = {2, 4, 6},$
$C = {2, 4, 6, 8, . . .}, D = {6}$

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Solution

$A = {x : x \in R and x satisfies x^{2} - 8 x + 12 = 0}$
2 and 6 are the only solutions of $x^{2} - 8 x + 12 = 0$ .
$∴ A = {2, 6}$
$B = {2, 4, 6}$
$C = {2, 4, 6, 8, . . . .}$
$D = {6}$
Clearly, $D \subset A \subset B \subset C$
Hence, $A \subset B, A \subset C, B \subset C, D \subset A, D \subset B, D \subset C$

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x^{2} - 8 x + 12 = 0}

B = {2, 4, 6}, C = {2, 4, 6, 8, . . . .}, D = {6}

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

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x^{2} - 8 x + 12 = 0

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