Question

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

Answer 1

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

Hence, $A ⊂ B, A ⊂ C, B ⊂ C, D ⊂ A, D ⊂ B, D ⊂ C$