CONCEPTS ON SETS AND THE DIFFERENT OPERATIONS INVOLVING SETS.pdf

Subject: Mathematics in the modern world

1. CONCEPTS ON SETS AND
THE DIFFERENT
OPERATIONS INVOLVING
SETS

2. CONCEPTS OF SET
•SETS IN MATHEMATICS, ARE SIMPLY A COLLECTION OF DISTINCT
OBJECTS FORMING A GROUP.
•A SET CAN HAVE ANY GROUP OF ITEMS, BE IT A COLLECTION OF
NUMBERS, DAYS OF A WEEK, TYPES OF VEHICLES, AND SO ON.
•EVERY ITEM IN THE SET IS CALLED AN ELEMENT OF THE SET.

3. DIFFERENT OPERATIONS ON
SETS

4. DIFFERENT OPERATIONS ON SETS
A. UNION SET
IN SET THEORY, THE UNION OF A COLLECTION OF SETS IS THE SET OF
ALL ELEMENTS IN THE COLLECTION. IT IS ONE OF THE FUNDAMENTAL
OPERATIONS THROUGH WHICH SETS CAN BE COMBINED AND
RELATED TO EACH OTHER.

5. DIFFERENT OPERATIONS ON SETS
B. INTERSECTION
THE INTERSECTION OF SETS IS THE SET OF ELEMENTS WHICH ARE
COMMON TO THE GIVEN SETS. IN SET THEORY, FOR ANY TWO SETS
A AND B, THE INTERSECTION IS DEFINED AS THE SET OF ALL THE
ELEMENTS IN SET A THAT ARE ALSO PRESENT IN SET B.

6. DIFFERENT OPERATIONS ON SETS
D. DIFFERENCE
WHAT IS THE DIFFERENCE OF SETS? THE DIFFERENCE BETWEEN THE
TWO SETS, A AND B, WRITTEN AS A ∖B OR A −B, IS A SET THAT
CONTAINS THOSE ELEMENTS OF A THAT ARE NOT IN B. TO FIND THE
DIFFERENCE, WE REMOVE ALL THE ELEMENTS OF SET B FROM SET A.
THE RESULTING SET CONSISTS OF THE REMAINING ELEMENTS
EXCLUSIVE TO SET A.

7. DIFFERENT OPERATIONS ON SETS
C. COMPLEMENT
THE COMPLEMENT OF A SET IS THE SET THAT INCLUDES ALL THE
ELEMENTS OF THE UNIVERSAL SET THAT ARE NOT PRESENT IN THE
GIVEN SET. LET’S SAY A IS A SET OF ALL COINS WHICH IS A SUBSET
OF A UNIVERSAL SET THAT CONTAINS ALL COINS AND NOTES, SO
THE COMPLEMENT OF SET A IS A SET OF NOTES.

8. UNIVERSAL SET
A UNIVERSAL SET (USUALLY DENOTED BY U) IS A SET WHICH HAS
ELEMENTS OF ALL THE RELATED SETS, WITHOUT ANY REPETITION OF
ELEMENTS. SAY IF A AND B ARE TWO SETS, SUCH AS A = {1,2,3} AND
B = {1,A,B,C}, THEN THE UNIVERSAL SET ASSOCIATED WITH THESE
TWO SETS IS GIVEN BY U = {1,2,3,A,B,C}.