Set Theory Discrete Mathematics Study Notes (Part-2)

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Set Theory Discrete Mathematics Study Notes (Part-2)- Set Theory topic comes under discrete mathematics which is conducted in 2 parts second part includes Function & types, domain & codomain, Lattice Theory.

This topic is important for various competitive exams such as GATE CSE, SSC JE, ISRO, ESE, IES and other computer science exams.

Table of content

1. Function
2. Domain and Codomain
3. Types of Functions
4. Function Composition
5. Lattice Theory
6. Types of Lattice Theory

Function

Definition: Let A and B be two non-empty sets. A function f from A to B is an assignment of exactly one element of B to each element of A. We write f (a) = b if b is that the unique element of B assigned by the function f to the element a of A. If f may be a function from A to B, we write f: A → B.

Domain and Codomain

If f is a function from A to B, then we may say that A is the domain of f and B is the codomain of f.

If f (a) = b, we are saying that b is that the image of a and a maybe a preimage of b. The range, or image, off such that it’s the set of all images of elements of A. Also, if f may be a function from A to B, we are saying that f maps A to B. A function f maps A to B.