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) $D=\left\{x\in R:x^3-6x^2+11x-6=0\right\}$.

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