Let \( X = \{-1, 0, 1\} \) and \( Y = \{1, 2, 3\} \). The function \( f: X \rightarrow Y \) defined by \( f = \{(-1, 1), (0, 1), (1, 2)\} \) is:- \( \bigcirc \) onto, but not 1-1- \( \bigcirc \) 1-1, but not onto- \( \bigcirc \) both 1-1 and onto- \( \bigcirc \) neither 1-1 or onto

Answered: Let X={-1,0,1} and Y={1,2,3}. The…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Let \( X = \{-1, 0, 1\} \) and \( Y = \{1, 2, 3\} \). The function \( f: X \rightarrow Y \) defined by \( f = \{(-1, 1), (0, 1), (1, 2)\} \) is:

- \( \bigcirc \) onto, but not 1-1
- \( \bigcirc \) 1-1, but not onto
- \( \bigcirc \) both 1-1 and onto
- \( \bigcirc \) neither 1-1 or onto

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1-1 (one-one) and onto functions

An injective function in mathematics is a function f that maps different items in its domain to different elements, so that f = f implies x₁ = x₂. It is sometimes referred to as a injection function or one-one (1-1) function. To put it another way, each member of the function's codomain is, at most, a single instance of an element from its domain.

A surjective function in discrete mathematics is a function f such that any element y can be mapped from element x such that f(x) = y. It is sometimes referred to as a surjection function or an onto function. In other words, each member of the function's codomain is an exact replica of one or more of its domain elements.

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