Home
Class 11
MATHS
Which of the following pairs of sets are...

Which of the following pairs of sets are disjoint ?
(i) `{1,2,3,4}` and {x : x is natural number and `4 le x le 6`}
(ii) `{a,e,i,o,u} and {c,d,e,f}`
(iii) {x : x is an even inetger} and {x : x is an odd inetger}.

Text Solution

Verified by Experts

(i) `{1,2,3,4}` and {x : x is a natural number and `4 le x le 6} = {4,5,6}`
`:.` 4 is common element in the two sets
Therefore, pair of sets is not disjoint
(ii) `{a,e,i,o,u} and {c,d,e,f}`
`because` Element e is common is two sets
Therefore, pair of sets is not disjoint
(iii) {x : x is an even inetger} = {2,4,6,8,10,....}
{x : x is an odd integer} = {1,3,5,7,9,...}
`:.` No element is common in two sets
Therefore, pair of sets is disjoint.
Promotional Banner

Topper's Solved these Questions

  • SETS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 1.5|7 Videos

  • SETS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 1.6|8 Videos

  • SETS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 1.3|9 Videos

  • SEQUENCE AND SERIES

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|32 Videos

  • STATISTICS

    NAGEEN PRAKASHAN ENGLISH|Exercise MISCELLANEOUS EXERCISE|7 Videos

Similar Questions

Explore conceptually related problems

Which of the following pairs of sets are disjoint(i) {1, 2, 3, 4} and {x : x is a natural number and 4 lt=xlt= 6 }(ii) {a , e , i , o, u } and { c , d , e , f} (iii) {x : x is an even integer } and {x : x is an odd integer}

List all the elements of the following sets : (i) A = {x : x is an odd natural number} (ii) B = {x : x is an integer, x lies b/w -1/2 and 9/2 } (iii) C{x :x is an integer, x^2le4 } (iv) D={x: x is a letter in the word loyal} (v) E= {x: x is a month of a year not having 31 days} (vi) F = {x : x is a consonant in the English alphabet which precedes k }.

Find the union of each of the following pairs of sets :(i) X= {1, 3, 5} Y= {1, 2, 3} (ii) A = [a , e , i , o, u} B = [a , b , c} (iii) A = {x : x is a natural number and multiple of 3} B = {x : x is a natural number less than 6} (iv) A = {x : x is a natural number and 1 (v) A = {1, 2, 3}, B = φ

Which of the following sets are equal ? A={x:x inN,xlt4},B=(1,1,2,3,3},C={1,3},D={x:x is an odd natural number lt5} E={1,2,3},F={1,1,3}

Which of the following are the examples of the null set ? (i) Set of odd natural numbers divisible by 2 (ii) Set of even prime numbers (iii) {x : x is a natural numbers, x lt 5 and x gt 7 } (iv) {y : y is a point common to any two parallel lines}.

For each of the following pairs of sets , identify the disjoint and overlapping sets: A = { x: x is a prime number , x lt 8 } B = {x: x is an even natural number , x lt 8 } .

For each of the following pairs of sets , identify the disjoint and overlapping sets: E = {x: x 4n, n in N } and F = {x: x = 9 n , n in N }

Taking the set of natural numbers as the universal set, write down the complements of the following sets: (i) {x : x is an even natural number} (ii) { x : x is an odd natural number } (iii) {x : x is a positive multiple of 3} (iv) { x : x is a prime number } (v) {x : x is a natural number divisible by 3 and 5} (vi) { x : x is a perfect square } (vii) { x : x is a perfect cube} (viii) { x : x + 5 = 8 }(ix) { x : 2x + 5 = 9} (x) { x : x ≥ 7 }(xi) { x : x ∈ N and 2x + 1 > 10 }

Match each of the set on the left in the roster form with the same set on the right described in set builder form: (i) {1, 2, 3, 6} (a) {x : x is a prime number and a divisor of 6} (ii) {2, 3} (b) {x : x is an odd natural number less than 10} (iii) {M,A,T,H,E,I,C,S} (c) {x : x is natural number and divisor of 6} (iv) {1, 3, 5, 7, 9} (d) {x : x is a letter of the word MATHEMATICS}.

Which of the following are the examples of empty set ? (i) {x:x in N,xlt7and xgt9} (ii) {x : x is a common point of two perpendicular lines} (iii) {x : x is an even natural number divisible by 3} (iv) {x : x^(2) = 4 and x " is an odd number"} .