Set Theory Part (2)

VENN Diagram

Often pictures are very helpful in our thinking. In set theory we use closed curves (usually circles) and rectangles to represent sets and a combination of these is named as Venn Diagram.

Examples of Venn diagram:

 ∪= Universal Set

 A= Subset of ∪

 A’= Complement of A

Universal Set with 2 disjoint sets A & B

∪= Real numbers

A= Odd numbers

B= Even numbers

Universal set with two intersecting sets A & B

∪= Real numbers

A= Odd numbers

B= Even numbers

Example 1:

Vanessa likes = {Apple, Grape, Orange, Dates, Melon}     Jessy likes = {Apple, Dates, Mango, Pear}

Vanessa’s likes ∪ Jessy’s likes

Vanessa’s likes ⋂ Jessy’s likes

Example 2:

In a baking class of 50 students, 17 take Chocolate cakes, 21 take Vanilla cakes, and 4 take both Chocolate cakes and Vanilla cakes. How many students in the baking class are not enrolled in either Chocolate cakes nor Vanilla cakes?

Note: X is students not enrolled Chocolate cakes nor Vanilla cakes.

13 + 4 + 17 + X = 50 students

42 + X = 50 students

X = 8 students