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Home » A, B and C are subsets of Universal Set U. If A = {2, 4, 6, 8, 12, 20}, B = {3, 6, 9, 12, 15}, C = {5, 10, 15, 20} and U is the set of all whole numbers, draw a Venn diagram showing the relation of U, A, B and C.
A, B and C are subsets of Universal Set U. If A = {2, 4, 6, 8, 12, 20}, B = {3, 6, 9, 12, 15}, C = {5, 10, 15, 20} and U is the set of all whole numbers, draw a Venn diagram showing the relation of U, A, B and C.
CBSE | Class 11 | Maths | NCERT Exemplar | Sets
A, B and C are subsets of Universal Set U. If A = {2, 4, 6, 8, 12, 20}, B = {3, 6, 9, 12, 15}, C = {5, 10, 15, 20} and U is the set of all whole numbers, draw a Venn diagram showing the relation of U, A, B and C.

Solution:

As per the question,

A=\{2,4,6,8,12,20\}, B=\{3,6,9,12,15\}, C=\{5,10,15,20\}

U is a universal set here

Hence,

\begin{array}{l} \Rightarrow \mathrm{A} \cap \mathrm{B}=\{2,4,6,8,12,20\} \cap\{3,6,9,12,15\} \\ =\{6,12\} \\ \Rightarrow \mathrm{B} \cap \mathrm{C}=\{3,6,9,12,15\} \cap\{5,10,15,20\} \\ =\{15\} \\ \Rightarrow \mathrm{A} \cap \mathrm{C}=\{2,4,6,8,12,20\} \cap\{5,10,15,20\} \\ =\{20\} \\ \Rightarrow \mathrm{A} \cap \mathrm{B} \cap \mathrm{C}=\{2,4,6,8,12,20\} \cap\{3,6,9,12,15\} \cap\{5,10,15,20\} \\ =\{\} \end{array}

As a result, the Venn diagram showing relation of the provided sets is:

NCERT Exemplar Class 11 Maths Chapter 1-4

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