Difference Of Sets

Author: Math Help

Here we are going to learn about an operatation on set called difference of sets.In mathematics, A set can have a limited  number of elements.Set is a collection of data.We can perform many operations on set.The difference operation is one of them.The subtract(difference) symbol in the  function represents the removal of the values from the second set from the first set. The operation of subtraction  is a removing or taking away objects from group of object.


Explanation of difference of two sets

Difference of sets is  defined as a method of rearrange  sets by removing the elements which belong to another sets. Difference of sets is a denoted  by either of the symbols – or \. P minus Q is can be written either P – Q or    P \ Q.

The differences  of two sets P and Q, is written as P-Q.it contains  contains that  elements of P which are not present  in elements of Q. here result  P-Q is obtained take set P as usual and compare with set Q. now remove those element in set P which matches with set Q.  If P={a,b,c,d}and Q={d,e}, then P-Q={a,b,c}.


Definition for difference of sets

The difference between the two sets A and B represented in the order as the set of all those elements of A which are not in B. It is denoted by A-B.

In symbol we write it as

A-B = {x :`x in A` and `x !in B`   }

similarly  B-A =   {  x  :   `x in B` and `x!in A`  }

By representing it in the venn diagram,


Examples problems

Below are the problems based on difference of sets -

Problem 1:

Consider the two sets A = {11,12, 13, 14, 15, 16}, B = {12, 14, 16, 18} find the difference between the  two sets?

Solution:

Given A = {11,12, 13, 14, 15, 16}

B = {12, 14, 16, 18}

A –B = {11, 13, 15}

B –A = {18}

The set of all elements are present in A or in B. But not in both is called the symmetric difference set.


Problem 2:

A={2,3,4,1,8,9}   B={2,3,4,1,8,,12},What is the A-B and B-A?

Solution:

Given A={2,3,4,1,8,9}

B={2,3,4,1,8,12}

Here all elements of A  is available in B except 9.

So the difference A-B ={ 9 }.

Here all elements of B  an available in A except 12.

So the difference B-A = {12 }.



Example 3:

Consider two sets A={a,b,f,g,h}, B={f,g,a,k} find A-B and B-A?

Solution:

Given  A = { a , b , f , g , h }

B = { f , g , a , k }

so   A-B  = { b , h }

and  B-A = { k }


Problem 4:

Consider given sets P={19,38,57,76,95} Q={7,19,57,75,94} Find P-Q and Q-P

Solution:

Given P = {19,38,57,76,95}

Q = {7,19,57,75,94}

so P-Q = {38,76,95}

and Q-P = {7,75,94}

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