Which of the following sets are equal?

A set is said to be equal with another set if all elements of both the sets are equal and same.

A = {1, 2, 3}

B ={x ∈ R: x²–2x+1=0}

x²–2x+1 = 0

(x–1)² = 0

∴ x = 1.

B = {1}

C= {1, 2, 2, 3}

In sets we do not repeat elements hence C can be written as {1, 2, 3}

D = {x ∈ R: x³ – 6x²+11x – 6 = 0}

For x = 1, x²–2x+1=0

= (1)³–6(1)²+11(1)–6

= 1–6+11–6

= 0

For x =2,

= (2)³–6(2)²+11(2)–6

= 8–24+22–6

= 0

For x =3,

= (3)³–6(3)²+11(3)–6

= 27–54+33–6

= 0

∴ D = {1, 2, 3}

Hence, the set A, C and D are equal.