Which of the following sets are equal? (i) A = {1, 2, 3} (ii) B = {x ∈ R:x2–2x+1=0} (iii) C = (1, 2, 2, 3} (iv) D = {x ∈ R : x3 – 6×2+11x – 6 = 0}.
Which of the following sets are equal? (i) A = {1, 2, 3} (ii) B = {x ∈ R:x2–2x+1=0} (iii) C = (1, 2, 2, 3} (iv) D = {x ∈ R : x3 – 6×2+11x – 6 = 0}.

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