Complement Of The Intersection Of Sets

The complement of the set X ∩ Y is the set of elements that are members of the universal set U but not members of X ∩ Y. It is denoted by (X ∩ Y) ’

Example:
Suppose U = set of positive integers less than 10,

X = {1, 2, 5, 6, 7} and Y = {1, 3, 4, 5, 6, 8} .

a) Draw a Venn diagram to illustrate ( X ∩ Y ) ’

b) Find ( X ∩ Y ) ’

Solution:
a) First, fill in the elements for X ∩ Y = {1, 5, 6}

Fill in the other elements for X and Y and for U

Shade the region outside X ∩ Y to indicate (X ∩ Y ) ’

b) We can see from the Venn diagram that

(X ∩ Y ) ’ = {2, 3, 4, 7, 8, 9}

Or we find that X ∩ Y = {1, 5, 6} and so

(X ∩ Y ) ’ = {2, 3, 4, 7, 8, 9}

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