1.

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»

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


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