Question -
Answer -
A set is said to be equal with another set if all elements of both thesets 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.