When all the elements of two sets are similar, then those two sets are considered to be the same.
(i) A = {1, 2, 3}
(ii) B ={x ∈ R: x2–2x+1=0}
x2–2x+1 = 0
(x–1)2 = 0
∴ x = 1.
B = {1}
(iii) C= {1, 2, 2, 3}
By excluding the repeated number,
C = {1, 2, 3}
(iv) D = {x ∈ R: x3 – 6x2+11x – 6 = 0}
If x = 1,
x2–2x+1=0
x2–2x+1 = (1)3–6(1)2+11(1)–6
x2–2x+1= 1–6+11–6
∴ x2–2x+1 = 0
If x =2,
x2–2x+1=0
x2–2x+1 = (2)3–6(2)2+11(2)–6
x2–2x+1 = 8–24+22–6
∴ x2–2x+1 = 0
If x =3,
x2–2x+1 = 0
x2–2x+1 = (3)3–6(3)2+11(3)–6
x2–2x+1 = 27–54+33–6
∴ x2–2x+1 = 0
D = {1, 2, 3}
Equal Sets = A, C, D