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