Discrete math (sets)
- 1. SETS Submitted to Md. Auhidur Rahman Lecturer Institute of Information & Technology Presented by Nadim Bhuiyan(ASH1825034M) Saifur Rahman(ASH1825031M) Fazle Rabbi(ASH1825004M) Mahabub (ASH1825003M)
- 2. Contents Definition of Sets Kinds of sets Venn Diagrams Operation on sets Laws of sets
- 3. Definition of sets: A set is a simply well defined list or collection distinct objects.The objects in a set is called element or member of the set. A set is an abstract data type that can store certain values,without any particular order, and no repeated values, A set is a group or collection of objects or number considered as an entity unto itself. For Example: • a set of chairs, • the set of nobel laureates in the worlds, • the set of integers, • the set of natural numbers less than 10, • the set of books in the table.
- 4. Kinds of sets Empty Set Finite Set Infinite Set Sub Set Disjoint Set Equality Set Union Set Intersection Set
- 5. Disjoint Set: Two set are called disjoint if their intersection is the empty set. let A and B be the set,then the disjoint set is A ∩ B= { } Equal set: Two set A and B are said to be equal or A=B if and only if A ⊆ B. and B ⊆ A . let A and B the set ,then the equal set is ,A={1,2,3,4,5} B={1,2,3,4,5} Union Set: The union of two sets A and B is the set of all elements belonging to A or B or both. let A and B the set ,then the union set is A U B.
- 6. Empty set: Any set that has no element in it is called an empty set or null set. let, A is a set then we denote it empty set A= Ø or { } Finite set: A set is called finite if it’s elements are equal in number to some specifiable nonnegative integers. let,A is a set ,then finite set A={2,3,4,5,6} Infinite set: A set is called infinite if the number of it’s elements is greater than any positive integer. let,A is a set ,then finite set A={2,3,4,5,6…….} Sub set: If every element of the set A is also an element of the B. Then A is said to be a sub set of B. let A and B the set , A is a subset of B, denoted by A ⊆ B. •
- 7. Venn Diagrams A helpful scheme to illustrate the relationship between sets and set operation is the Venn Diagram.
- 8. Operation on Sets Union,U. AUB is the set of all elements that are in A OR B. Intersection ∩ . A ∩ B is the set of all elements that are in A AND B.
- 9. Operation of sets Complement A is the set ,we denoted it A’ or A∁ .
- 10. Laws of sets 1. Commutative Laws: • For any two finite sets A and B; (i) A U B = B U A (ii) A ∩ B = B ∩ A 2. Associative Laws: • For any three finite sets A, B and C; (i) (A U B) U C = A U (B U C) (ii) (A ∩ B) ∩ C = A ∩ (B ∩ C)
- 11. Laws of sets 3. Idempotent Laws: • For any finite set A; (i) A U A = A (ii) A ∩ A = A 4. Distributive Laws: • For any three finite sets A, B and C; (i) A U (B ∩ C) = (A U B) ∩ (A U C) (ii) A ∩ (B U C) = (A ∩ B) U (A ∩ C) 5.De Morgan’s Laws : For any three finite sets A, B ; (i) (A U B)’ = A' ∩ B' (ii) (A ∩ B)’ = A' U B'