Mathematics for Biotechnology and Data Science
Chapter 3: Application of Set Theory
Chapter 6: MAPPING OR FUNCTIONS
Chapter 8: Inverse of a Function
Chapter 2: Operation of Sets
2.1. Union of Sets: Let A and B be two sets. The union of A and B is the set of all those elements which belong either to A or to B or to both A and B.
We shall use notation 
(reads as “A union B”) to denote the union of
A and B.
Thus,
.
Clearly, 
.
and,
.
It is evident form the
definition that 
Example 1: If
A = {1, 2, 3} and B = {1, 3, 5, 7}, then 
.
Example 2: If
and 
then
2.2. Intersection of Sets: Let A and B be two sets. The intersection of A and B is the set of all those elements that belong to both A and B.
We
shall use notation 
(reads as “A intersection B”) to denote the
intersection of A and B.
Thus,
.
Clearly,
.
Example
3: If
A = {1, 2, 3, 4, 5} and B = {1, 3, 9, 12}, then
.
Example
4: If
and 
then
Example
5: If
and 
then find .
Solution:
We
have, 
x is multiple of 3 and x is a multiple of 4
x is a multiple of 3 and 4 both
x is multiple of 12
Hence,
.
2.3. Complement Sets:
Let
U be the universal set and let A be a set such that 
. Then the complement
of A with respect to U is denoted by 
or 
or 
and defined the set of all those elements of U
which are not in A.
Thus 
.
Clearly 
Example 7: Let
the set of natural numbers N = {1, 2, 3, 4,…} be the universal set and let A =
{2, 4, 6, 8,…} then 
.
Example 8: If
U = {1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {1, 3, 5, 7, 9} then 
.
EXERCISE
|
Q:1
If A and B are two sets such that Ans (1) A (2) B |
|
Q:2 If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11} and D = {10, 11, 12, 13, 14} then Find
(1) (2) (3) (4) (5) (6) (7) (8)
(9) (10) Ans (1) {1, 2, 3, 4, 5, 6, 7, 8} (2) {1, 2, 3, 4, 5, 7, 8, 9, 10, 11} (3) {4, 5, 6, 7, 8, 9, 10, 11} (4) {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14} (5) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} (6) {1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14} (7) {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14} (8) {4, 5} (9) (10) {4, 5,10,11} |
|
Q:3
Let
Find
(1) (2) (3) (4) B (5) B (6) C Ans
(1)
B (2) C (3) D (4) |
|
Q:4 If A = {3, 6, 12, 15, 18, 21}, B = {4, 8, 12 , 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16} and D = {5, 10, 15, 20} then Find
(1) A (2)
A (3) A (4) B (5) C (6) D Ans (1) {12} (2) {2, 3, 4, 6, 8, 10, 12, 14, 15, 16, 18, 21} (3){3, 5, 6, 10, 12, 15, 18, 20, 21} (4) {3, 6, 12, 15, 18, 21, 4, 8, 16, 20} (5){6, 12} (6) {15} |
|
Q:5 Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6} then Find
(1) (2) (3) (4) (5) Ans (1) {5, 6, 7, 8, 9} (2) {1, 3, 5, 7, 9} (3){ 1, 2, 5, 6, 7, 8, 9} (4) {5, 7, 9} (5) A |
|
Q:6 Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7} then verify
that (1) (2) |
continued ..................