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: x^{2}–2x+1=0}

x^{2}–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: x^{3} – 6x^{2}+11x – 6 = 0}

For x = 1, x^{2}–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.

Answered by Sakshi | 1 year agoFind the symmetric difference A Δ B, when A = {1, 2, 3} and B = {3, 4, 5}.