Question

intersection of sets 5 examples​

Answer 1

Answer:

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Answer 2

Intersection of Sets

The intersection of sets A and B can be defined as a new set containing common elements of A and B.

Let us assume we have two sets, A and B, then their intersection results in a new set containing all the common elements between A and B.

Example 1

You are given two sets, defined as follows:

A = {1, 4, 8, 9}

B = {3, 4, 9}

Write down the intersection of the sets.

Solution:

As we know, that intersection of two sets is the set containing the common elements of both the sets; therefore, our new set is going to be:

{4, 9}

We can observe that 4 and 9 are the only common elements to both A and B. So the set which contains both these elements will be the intersection of sets.

The Notation for Intersection of Sets

Delving further into the intersection of sets, our next step is to talk about the notation used to represent sets’ intersection. The intersection between any two sets, A and B, is represented by the symbol ‘∩’. Like the symbol used for the union of sets, this symbol is used between the operands. The operands, in this case, are the names denoting the sets.

This method of notation is called the ‘infix notation.’ In this notation, the operator is surrounded by the operands. The operator, in our case, is ‘∩’. It is, most commonly, used to refer to binary operations. We know that intersection, as the union of sets, is also a binary operation.

An example of this would be as follows:

A = {0, 0, 0, 4}

B = {2, 6, 9}

Then the intersection of these sets is denoted by:

A ∩ B

So, whenever we want to express the intersection between two sets, this is how we do it symbolically. It is an expression of set A intersecting set B.

Let’s solve some examples to understand the intersection of sets.

Example 2

If sets A and B are defined as:

A = {1, 12, 14, 11, 13, 7, 9, 17, 19}

B = {12, 15, 14, 2, 1, 6, 9, 0}

Find out the intersection of set A and B.

Solution:

The intersection of two sets is defined as the set containing elements in set A which are also present in set B; in other words, the common elements.

As we can see, 12, 14, 1, 9 are the elements present in both set A and set B. So, we have the intersection of sets equal to:

A ∩ B = {12, 14, 1, 9}