# 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