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

7th Grade Math Problems

8th Grade Math Practice

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