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}.

Asked by Aaryan | 1 year ago |  40

##### Solution :-

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, 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.

Answered by Sakshi | 1 year ago

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