Sets Intersection: Intersection Of Two Sets

The intersection of two sets X and Y is the set of elements that are common to both set X and set Y. It is denoted by X ∩ Y and is read ‘X intersection Y’.

Example:
Draw a Venn diagram to represent the relationship between the sets

X = {1, 2, 5, 6, 7, 9, 10} and Y = {1, 3, 4, 5, 6, 8, 10}

Solution:
We find that X ∩ Y = {1, 5, 6, 10} ← in both X and Y

For the Venn diagram,

Step 1 : Draw two overlapping circles to represent the two sets.

Step 2 : Write down the elements in the intersection.

Step 3 : Write down the remaining elements in the respective sets.

Notice that you start filling the Venn diagram from the elements in the intersection first.

If X ⊂Y then X ∩Y = X . We will illustrate this relationship in the following example.

Example:
Draw a Venn diagram to represent the relationship between the sets

X = {1, 6, 9} and Y = {1, 3, 5, 6, 8, 9}

Solution:
We find that X ∩ Y = {1, 6, 9} which is equal to the set X

For the Venn diagram,

Step 1 : Draw one circle within another circle

Step 2 : Write down the elements in the inner circle.

Step 3 : Write down the remaining elements in the outer circle.

Sometimes, the two given sets may not have any common elements. Set X and set Y are called disjoint sets if X ∩ Y = Ø.

Example:
Draw a Venn diagram to represent the relationship between the sets

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

Solution:
We find that X ∩ Y = Ø.

For the Venn diagram, draw two separate circles with their respective members.

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