Which of the following sets are equal? A = 1 , 2 , 3 , B = x ∈ R : x 2 - 2 x + 1 = 0 , C = 1 , 2 , 2 , 3 , D = x ∈ R : x 3 - 6 x 2 + 11 x - 6 = 0

A set is said to be equal with another set if all elements of both the sets are equal and having same number of elements. A = { 1 , 2 , 3 } B = x ∈ R : x 2 - 2 x + 1 = 0 ⇒ x 2 - 1 x - 1 x + 1 = 0 ⇒ x - 1 x - 1 = 0 ⇒ 1 , 1 C = 1 , 2 , 2 , 3 = 1 , 2 , 3 D = x ∈ R : x 3 - 6 x 2 + 11 x - 6 = 0 , Substitute the elements of the set C in the equation x 3 - 6 x 2 + 11 x - 6 = 0 , We can see that the elements of set C are the zero's of the above polynomial Therefore, D = 1 , 2 , 3 . Therefore, A , C and D are equal.

Which of the following sets are equal? A = { x : x ∈ N , x < 3 } , B = { 1 , 2 } , C = { 3 , 1 } D = { x : x ∈ N , x is odd, x < 5 } , E = { 1 , 2 , 1 , 1 } , F = { 1 , 1 , 3 }

First we need to represent all the given sets in roster method Given A = { x : x ∈ N , x < 3 } ⇒ A = { 1 , 2 } B = { 1 , 2 } C = 3 , 1 D = { x : x ∈ N , x is odd, x < 5 } ⇒ D = 1 , 3 (since, the odd natural numbers less than 5 are 1 and 3 ) E = { 1 , 2 } (since, repetition is not allowed) F = { 1 , 3 } (since, repetition is not allowed) Any two sets are if and only if they have same elements and same cardinality ∴ Sets A , B and E are equal and C , D and F are equal.

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MATHEMATICS for CLASS XI>Chapter 1 - Sets>EXERCISE 1.3

R D Sharma Solutions for Chapter: Sets, Exercise 3: EXERCISE 1.3

Author:R D Sharma

R D Sharma Mathematics Solutions for Exercise - R D Sharma Solutions for Chapter: Sets, Exercise 3: EXERCISE 1.3

Attempt the practice questions on Chapter 1: Sets, Exercise 3: EXERCISE 1.3 with hints and solutions to strengthen your understanding. MATHEMATICS for CLASS XI solutions are prepared by Experienced Embibe Experts.