Q. 94.1( 61 Votes )

# Given the sets A

A universal set is a set which contains all the elements of its subsets. So if there are two sets with some members then the universal set containing those two sets, will have elements will all the members of both sets without repetition.

(i) Given: A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}

Now, let D = {0, 1, 2, 3, 4, 5, 6}

Since, 8 belongs to C then its universal set must contain 8, but D does not contain 8.

∴ D is not a universal set for A, B, C.

(ii) Given: A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}

Now, let D = ϕ

Since, D is an empty set it does not contain any element

∴ D is not a universal set for A, B, C.

(iii) Given: A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}

Now, let D = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Since, all the members of A, B, C belongs to D.

∴D is a universal set for A, B, C.

(iv) Given: A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}

Now, let D = {1, 2, 3, 4, 5, 6, 7, 8}

Since, 0 belongs to C but it is not a member of D.

∴ D is not a universal set.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

If U = {2, 3, 5, RD Sharma - Mathematics

If U = {1, 2, 3, RS Aggarwal - Mathematics

If U = {2, 3, 5, RD Sharma - Mathematics

Fill in the blankMathematics - Exemplar

if U is the univeRS Aggarwal - Mathematics

If A = {1, 3, 5},RS Aggarwal - Mathematics

What universal seNCERT - Maths

Given the sets A NCERT - Maths