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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}.
Solution
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}
- Elements 2, 6 of set A are also in set B.
⇒ A ⊂ B - Thus, elements 2, 6 of set A are also in set C.
⇒ A ⊂ C - Elements 2, 4, 6 of set B are in set C.
⇒ B ⊂ C - 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.
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