Question:
Which of the following sets are equal?
(i) $A=\{1,2,3\}$;
(ii) $B=\left\{x \in R: x^{2}-2 x+1=0\right\}$;
(iii) $C=\{1,2,2,3\}$;
(iv) $D=\left\{x \in R: x^{3}-6 x^{2}+11 x-6=0\right\}$.
Solution:
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) $A=\{1,2,3\}$
(ii) $B=\left\{x \in R: x^{2}-2 x+1=0\right\}$
Set B would be {1}.
(iii) $C=\{1,2,2,3\}$
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) $D=\left\{x \in R: x^{3}-6 x^{2}+11 x-6=0\right\}$ includes elements $\{1,2,3\}$.
∴ D = {1, 2, 3}
Hence, we can say that A = C = D.