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
● Subset
8th Grade Math Practice
From Difference of Two Sets to HOME PAGE
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.
Dec 06, 23 01:23 AM
Dec 04, 23 02:14 PM
Dec 04, 23 01:50 PM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.