English

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}.

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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}.

Sum
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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}

  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.

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Chapter 1: Sets - Miscellaneous Exercise [Page 21]

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NCERT Mathematics [English] Class 11
Chapter 1 Sets
Miscellaneous Exercise | Q 1. | Page 21

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