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 – 6x2+11x – 6 = 0}.
NOTE: 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
= (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
As cubic equation has three roots at max so the roots are 1, 2, 3
∴ D = {1, 2, 3}
Hence Set A, C and D are equal.