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}.

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}
Factorize
x² - 8x + 12 = 0
x² - 6x -2x + 12 = 0
x(x - 6) -2(x-6) = 0
(x-6)(x-2) =0
x - 6 = 0 or x – 2 = 0
x is equal to 6 and 2
So that, A = {2, 6}
Given that B = {2, 4, 6}, C = {2, 4, 6, 8 …}, D = {6}
All element of set D lies in set A , all element of set of A lies in set B and all element of set B lies in set C.
D ⊂ A ⊂ B ⊂ C
D is subset of A, B and C . D ⊂ A, D ⊂ B, D ⊂ C ,
A is subset of B and C.
A ⊂ B, A ⊂ C
B is subset of C.
B ⊂ C
Hence total subsets are A ⊂ B, A ⊂ C, B ⊂ C, D ⊂ A, D ⊂ B, D ⊂ C.