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, x satisfies the equation x² – 8x + 12 = 0}

= {x : x ∈ R and (x - 6)(x - 2) = 0}

That means A = {2, 6}
B = {2, 4, 6}
C = {2, 4, 6, 8, ….}
D = {6}

1. Elements 2, 6 of set A are also in set B.
   ⇒ A ⊂ B
2. Thus, elements 2, 6 of set A are also in set C.
   ⇒ A ⊂ C
3. Elements 2, 4, 6 of set B are in set C.
   ⇒ B ⊂ C
4. Element 6 of set D is in all three sets A, B and C.
   ⇒ D ⊂ A, D ⊂ B, D ⊂ C

Now, A ⊂ B, A ⊂ C, B ⊂ C, D ⊂ A, D ⊂ B and D ⊂ C.