Which of the following sets are equal?A = {1, 2, 3}B = {x ∈ R : x2

1.	Which of the following sets are equal?A = {1, 2, 3}B = {x ∈ R : x2 – 2x+1=0}C = (1, 2, 2, 3}D = {x ∈ R : x3 – 6x2+11x – 6 = 0}.
Answer» The set is said to be equal with another set if all elements of both the sets are equal and same. Now, 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 thus C can be written as {1, 2, 3} D = {x ∈ R: x³ – 6x²+11x – 6 = 0} For the x = 1, x²–2x+1=0 = (1)³– 6(1)²+ 11(1) – 6 = 1–6+11–6 = 0 For the x =2, = (2)³–6(2)²+11(2)–6 = 8–24+22–6 = 0 For the x =3, = (3)³–6(3)²+11(3)–6 = 27–54+33–6 = 0 ∴ D = {1, 2, 3} Thus, the set A, C and D are equal.

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

Answer»

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

Now,

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 thus C can be written as {1, 2, 3}

D = {x ∈ R: x³ – 6x²+11x – 6 = 0}

For the x = 1, x²–2x+1=0

= (1)³– 6(1)²+ 11(1) – 6

= 1–6+11–6

= 0

For the x =2,

= (2)³–6(2)²+11(2)–6

= 8–24+22–6

= 0

For the x =3,

= (3)³–6(3)²+11(3)–6

= 27–54+33–6

= 0

∴ D = {1, 2, 3}

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