Two sets having identical elements are known as
a.
null sets
b. equal sets
C.
disjoint sets
d. None

2 thoughts on “Two sets having identical elements are known as<br />a.<br />null sets<br />b. equal sets<br />C.<br />disjoint sets<br />d. None”

1. Solution The required numbers are 1, 2, 3, 4, 5, 6. So, the given set in the roster form

   is {1, 2, 3, 4, 5, 6}.

   Example 3 Write the set A = {1, 4, 9, 16, 25, . . . }in set-builder form.

   Solution We may write the set A as

   A = {x : x is the square of a natural number}

   Alternatively, we can write

   A = {x : x = n2

   , where n ∈ N}

   Example 4 Write the set

   123456 { }

   234567

   ,,,,, in the set-builder form.

   Solution We see that each member in the given set has the numerator one less than

   the denominator. Also, the numerator begin from 1 and do not exceed 6. Hence, in the

   set-builder form the given set is

   where is a natural number and 1 6

   1

   n

   x:x , n n

   n

   ⎧ ⎫ ⎨ ⎬ = ≤≤ ⎩ ⎭ +

   Example 5 Match each of the set on the left described in the roster form with the

   same set on the right described in the set-builder form :

   (i) {P, R, I, N, C, A, L} (a) { x : x is a positive integer and is a divisor of 18}

   (ii) { 0 } (b) { x : x is an integer and x2 – 9 = 0}

   (iii) {1, 2, 3, 6, 9, 18} (c) {x : x is an integer and x + 1= 1}

   (iv) {3, –3} (d) {x : x is a letter of the word PRINCIPAL}

   Solution Since in (d), there are 9 letters in the word PRINCIPAL and two letters P and I

   are repeated, so (i) matches (d). Similarly, (ii) matches (c) as x + 1 = 1 implies

   x = 0. Also, 1, 2 ,3, 6, 9, 18 are all divisors of 18 and so (iii) matches (a). Finally, x2 – 9 = 0

   implies x = 3, –3 and so (iv) matches (b).

   EXERCISE 1.1

   1. Which of the following are sets ? Justify your answer.

   (i) The collection of all the months of a year beginning with the letter J.

   (ii) The collection of ten most talented writers of India.

   (iii) A team of eleven best-cricket batsmen of the world.

   (iv) The collection of all boys in your class.

   (v) The collection of all natural numbers less than 100.

   (vi) A collection of novels written by the writer Munshi Prem Chand.

   [tex]hope \: this \: will \: help \: you[/tex]

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2. Option b

   Step-by-step explanation:

   Given:–

   Two sets having identical elements

   To find:–

   What type of these sets ?

   Solution:–

   Two sets having identical elements then the two sets are called Equal sets .

   If A and B are having identical elements then both A and B are called equal sets and it is denoted by A=B.

   That means All elements in A are in B and all elements in B area also in A.

   Answer:–

   Two sets having identical elements then the two sets are called Equal sets .

   Options wise explanation:–

   Null sets :-

   A set having no element in it is called a null or void or empty set.

   Ex:-

   A is a set of whole numbers less than 0

   Dis joint sets:–

   If two sets having no elements in common then they are called Dis joint sets.

   If A and B are dis joint sets then AnB = { }

   n(AnB) = 0.

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