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}.
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}.
B = {x ∈ R : x2 – 2x+1=0}
C = (1, 2, 2, 3}
D = {x ∈ R : x3 – 6x2+11x – 6 = 0}.
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.