Which of the Following Sets are Equal?
| Set | Elements |
|---|---|
| (i) \[ A=\{1,2,3\} \] | \[ \{1,2,3\} \] |
| (ii) \[ B=\{x\in R:x^2-2x+1=0\} \] | \[ x^2-2x+1=0 \] \[ (x-1)^2=0 \] \[ B=\{1\} \] |
| (iii) \[ C=\{1,2,2,3\} \] | \[ \{1,2,3\} \] |
| (iv) \[ D=\{x\in R:x^3-6x^2+11x-6=0\} \] | \[ (x-1)(x-2)(x-3)=0 \] \[ D=\{1,2,3\} \] |
Conclusion
Since \[ A=\{1,2,3\}, \quad C=\{1,2,3\}, \quad D=\{1,2,3\} \]
Therefore,
\[ \boxed{A=C=D} \]