Set Theory Discrete Mathematics Study Notes (Part-2)

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.

         A function f maps A to B.

Types of Functions

Function Composition

Lattice Theory

Types of Lattice Theory

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