Question

Decide, among the following sets, which sets are subsets of one and another:
A = {x: x ∈ R and x satisfy x² – 8x + 12 = 0}, B = {2, 4, 6},
C = {2, 4, 6, 8…}, D = {6}.

Answer 1

A = {x: x ∈ R and x satisfies x²– 8x + 12 = 0}
2 and 6 are the only solutions of x² – 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