# Which of the following sets are equal?

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.

∴ = {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.