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 and x satisfy x² – 8x + 12 = 0}

Let us solve the quadratic equation

x² – 8x + 12 = 0

Let us proceed by using middle term factorisation.

x² – 2x - 6x + 12 = 0

x (x - 2) - 6 (x - 2) = 0

(x - 2) (x - 6) = 0

x - 2 = 0; x - 6 = 0

x = 2; x = 6

2 and 6 are the only solutions of x² – 8x + 12 = 0.

Now,

A = {2, 6}, B = {2, 4, 6},

C = {2, 4, 6, 8....}, D = {6}

We say that A is a subset of B if and only if all the elements of A are in B and in that case we write A ⊂ B.

Therefore,

D ⊂ A ⊂ B ⊂ C

Hence, A ⊂ B, A ⊂ C, B ⊂ C, D ⊂ A, D ⊂ B, D ⊂ C

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NCERT Solutions Class 11 Maths Chapter 1 Exercise ME Question 1

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 }.

Summary:

We are asked to decide, among the following sets, which sets are subsets of one and another: A = { x : x ∈ R and x satisfy x 2 – 8x + 12 = 0 }, B = { 2, 4, 6 }, C = { 2, 4, 6, 8, . . . }, D = { 6 }. We have found that the A ⊂ B, A ⊂ C, B ⊂ C, D ⊂ A, D ⊂ B, D ⊂ C.