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The Venn diagram

The Venn diagram is used to simplify solving problems in sets. It can

also be used to illustrate sets.

Example

Given that set A = {1, 2, 3, 4, 5} and B = {2, 4, 6, 8}. Use a Venn diagram

to find:

a) i) A n B

ii) n (A n B)

b) i) A U B

ii) n (A U B)

Solution

i) A n B = {2,4}

ii) n (A n B) = 2

b) i) A U B = {1,2,3,4,5,6,8}

ii) n (A U B) = 7**Example**

Given that P = {1, 3, 5, 7, 9, 11, 13, 15} and Q = {3, 9, 15}. Illustrate this

information in a Venn diagram.

Solution

Since Q < P , Q is drawn inside P.

P n Q = {3, 9,15} = Q

P U Q = {1, 3, 5, 7, 9,11,13,15} = p

Example

Given that, R = {2, 4, 6, 8} and S = {1, 3, 5, 7}. Show this information in

a Venn diagram.

Solution

Here R and S are disjoint sets i.e., R n S {} so R and S are drawn

separately as shown below