Question

Which of the following sets are equal? 

(i) \[A = \left\{ 1, 2, 3 \right\};\] 

(ii) \[B = \left\{ x \in R : x^2 - 2x + 1 = 0 \right\};\] 

(iii) \[C = \left\{ 1, 2, 2, 3 \right\};\] 

(iv) \[D = \left\{ x \in R : x^3 - 6 x^2 + 11x - 6 = 0 \right\}\]

Answer 1

Two sets A & B are equal if every element of A is a member of B & every element of B is a member of A. 

(i) \[A = \left\{ 1, 2, 3 \right\}\]

(ii) \[B = \left\{ x \in R : x^2 - 2x + 1 = 0 \right\}\] 

Set B would be {1}. 

(iii) \[C = \left\{ 1, 2, 2, 3 \right\}\] 

It can be written as {1, 2, 3} because we do not repeat the elements while writing the elements of a set.
∴ C = {1, 2, 3} 

(iv) \[D = \left\{ x \in R : x^3 - 6 x^2 + 11x - 6 = 0 \right\}\] includes elements {1, 2, 3}.
      ∴ D = {1, 2, 3}
Hence, we can say that A = C = D.