# Difference of Two Sets

How to find the difference of two sets?

If A and B are two sets, then their difference is given by A - B or B - A.

If A = {2, 3, 4} and B = {4, 5, 6}

A - B means elements of A which are not the elements of B.

i.e., in the above example A - B = {2, 3}

In general, B - A = {x : x
B, and x  A}

If A and B are disjoint sets, then A – B = A and B – A = B

Solved examples to find the difference of two sets:

1. A = {1, 2, 3} and B = {4, 5, 6}.

Find the difference between the two sets:

(i) A and B

(ii) B and A

Solution:

The two sets are disjoint as they do not have any elements in common.

(i) A - B = {1, 2, 3} = A

(ii) B - A = {4, 5, 6} = B

2. Let A = {a, b, c, d, e, f} and B = {b, d, f, g}.

Find the difference between the two sets:

(i) A and B

(ii) B and A

Solution:

(i) A - B = {a, c, e}

Therefore, the elements a, c, e belong to A but not to B

(ii) B - A = {g)

Therefore, the element g belongs to B but not A.

3. Given three sets P, Q and R such that:

P = {x : x is a natural number between 10 and 16},

Q = {y : y is a even number between 8 and 20} and

R = {7, 9, 11, 14, 18, 20}

(i) Find the difference of two sets P and Q

(ii) Find Q - R

(iii) Find R - P

(iv) Find Q – P

Solution:

According to the given statements:

P = {11, 12, 13, 14, 15}

Q = {10, 12, 14, 16, 18}

R = {7, 9, 11, 14, 18, 20}

(i) P – Q = {Those elements of set P which are not in set Q}

= {11, 13, 15}

(ii) Q – R = {Those elements of set Q not belonging to set R}

= {10, 12, 16}

(iii) R – P = {Those elements of set R which are not in set P}

= {7, 9, 18, 20}

(iv) Q – P = {Those elements of set Q not belonging to set P}

= {10, 16, 18}

Set Theory

Sets

Objects Form a Set

Elements of a Set

Properties of Sets

Representation of a Set

Different Notations in Sets

Standard Sets of Numbers

Types of Sets

Pairs of Sets

Subset

Subsets of a Given Set

Operations on Sets

Union of Sets

Intersection of Sets

Difference of two Sets

Complement of a Set

Cardinal number of a set

Cardinal Properties of Sets

Venn Diagrams

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles 1. ### 2nd grade math Worksheets | Free Math Worksheets | By Grade and Topic

Dec 06, 23 01:23 AM

2nd grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students.

2. ### Rupees and Paise | Paise Coins | Rupee Coins | Rupee Notes

Dec 04, 23 02:14 PM

Money consists of rupees and paise; we require money to purchase things. 100 paise make one rupee. List of paise and rupees in the shape of coins and notes: