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