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}.
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, \(A ⊂ B, A ⊂ C, B ⊂ C, D ⊂ A, D ⊂ B, D ⊂ C\)