SET, RELATION, FUNCTION AND BINARY OPERATIONS
I Number System
1. Natural numbers N = {1, 2, 3, 4.................}
2. Whole numbers W = {0, 1, 2, 3................}
3. Integers I (z) = {...........-3, -2, -1, 0, 1, 2, 3..............}
4. Rational numbers Q = p , p,q I,q 0 q 5. Irrational
numbers = 2, 3,.............e, ........
6. Real numbers R = The union of rational and irrational numbers. Note : N W
Z Q R C II.
Types of Sets 1
. Finite set - Contains finite number of elements
2. Infinite set - Contains infinite number of elements
3. Empty set (void set), (Null set) - Contains no element
4. Singleton set - Contains one element
5. Equivalent set - If n A n B b g b g then A and B are equivalent
6. Equal set - A B and B A A B
7. Subset and super set - every element of A is an element of B then A B and
BA
8. Proper subset - A is a subset of B and A B then A is a proper sub set of B
and is denoted as A B
9. Power set - The set of all subsets of A is the power set of A and is denoted
as P A let A b g, , , l1 2 3q P Ab g ml1 2 3 1 2 1 3 2 3 1 2 3
q, , , , , , , , , , , , l q l q l q l q l q l q r 6 10. Universal set - In any discussion
in set theory we consider a set which is the superset of all the sets under
consideration is called the universal set III.
Set operations
1. Union - A B {x / x A or x B}
2. Intersection - A B {x / x A and x B} , If A B then A and B
are disjoint.
3. Complement - C A {x / x A and x U} , U is the universal set
4. Difference - C C A B {x / x A and x B} x / x A andx B A B
I Number System
1. Natural numbers N = {1, 2, 3, 4.................}
2. Whole numbers W = {0, 1, 2, 3................}
3. Integers I (z) = {...........-3, -2, -1, 0, 1, 2, 3..............}
4. Rational numbers Q = p , p,q I,q 0 q 5. Irrational
numbers = 2, 3,.............e, ........
6. Real numbers R = The union of rational and irrational numbers. Note : N W
Z Q R C II.
Types of Sets 1
. Finite set - Contains finite number of elements
2. Infinite set - Contains infinite number of elements
3. Empty set (void set), (Null set) - Contains no element
4. Singleton set - Contains one element
5. Equivalent set - If n A n B b g b g then A and B are equivalent
6. Equal set - A B and B A A B
7. Subset and super set - every element of A is an element of B then A B and
BA
8. Proper subset - A is a subset of B and A B then A is a proper sub set of B
and is denoted as A B
9. Power set - The set of all subsets of A is the power set of A and is denoted
as P A let A b g, , , l1 2 3q P Ab g ml1 2 3 1 2 1 3 2 3 1 2 3
q, , , , , , , , , , , , l q l q l q l q l q l q r 6 10. Universal set - In any discussion
in set theory we consider a set which is the superset of all the sets under
consideration is called the universal set III.
Set operations
1. Union - A B {x / x A or x B}
2. Intersection - A B {x / x A and x B} , If A B then A and B
are disjoint.
3. Complement - C A {x / x A and x U} , U is the universal set
4. Difference - C C A B {x / x A and x B} x / x A andx B A B
