Difference between Union and Intersection

WELCOME Grade 9-11 Students

In today’s blog we are going to look at the difference between Union and Intersection. 

 

The union of two sets

The set made by combining the elements of two sets is known as union.  It is normally represented by the symbol ∪. The union of Sets A and B is the set of elements in A, or B or both.  The diagram below shows the universal set with set A and set B.  The shaded area is known to be the union between the two sets.  

Example of Union Set

If U= {11, 12, 13, 14, 15, 16, 17, 18}, A= {12, 15, 18} and B= {13, 15, 17}

Then A ∪ B= {12, 13, 15,17, 18} .

 

Intersection of two sets

The intersection of two sets has only the elements common to both sets.  This is normally represented by the symbol ∩. The intersection of Sets A and B is the set of all elements that are common to both A and B.  The diagram below shows that the shaded region is known to be the intersection.

Example of Intersection Set

If U= {11, 12, 13, 14, 15, 16, 17, 18}, A= {12, 15, 18} and B= {13, 15, 17}

Then A ∩ B= {15}

The difference between Union and Intersection of two sets

The symbols ∪ and ∩ were introduced by Giuseppe Peano where he took both symbols and used them for intersection and union in 1888 in ‘Calcolo geometrico’ which in English is Geometrical Calculus.  The main difference between union and intersection can be compared on the basis of their general definitions, mathematical definitions, symbolic representations, logical inferences, process characteristics and examples.  Once you know the difference it should be simple for you to answer any question about union and intersection. 

 

Practice Question

1.     If X= {1, 2, 3, 4, 5, 6, 7, 8, 9} and Y= { 2, 4, 6, 8, 10, 12, 14, 16, 18} then

a.     X ∪ Y=

b.     X ∩ Y=

 

2.     Find the union and intersection of the two given sets in each of the following:

a.     A= {3, 6, 9, 12, 15} and B= {6, 8,10, 12, 14}

b.     P= {1, 3, 5, 7, 11, 13} and Q= {1, 5, 11}