{d, e, f, g}. Define 8. Let X = {a, b, c} and Y = functions H and K by the arrow diagrams belov Domain of H Co-domain of H X Y Н a of • g
{d, e, f, g}. Define 8. Let X = {a, b, c} and Y = functions H and K by the arrow diagrams belov Domain of H Co-domain of H X Y Н a of • g
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The image presents a mathematical problem focused on defining functions \( H \) and \( K \) between sets \( X \) and \( Y \).
**1. Problem Statement:**
Let \( X = \{ a, b, c \} \) and \( Y = \{ d, e, f, g \} \). Define functions \( H \) and \( K \) using the arrow diagrams provided.
**2. Arrow Diagrams Explanation:**
- **Function \( H \):**
- **Domain of \( H \):** Set \( X \) with elements \( a, b, c \).
- **Co-domain of \( H \):** Set \( Y \) with elements \( d, e, f, g \).
- **Mappings of \( H \):**
- \( a \) maps to \( d \).
- \( b \) maps to \( f \).
- \( c \) maps to \( f \).
- **Function \( K \):**
- **Domain of \( K \):** Set \( X \) with elements \( a, b, c \).
- **Co-domain of \( K \):** Set \( Y \) with elements \( d, e, f, g \).
- **Mappings of \( K \):**
- \( a \) maps to \( d \).
- \( b \) maps to \( e \).
- \( c \) maps to \( g \).
**3. Understanding the Functions:**
The arrows in each diagram illustrate how elements in the domain \( X \) are associated with elements in the co-domain \( Y \) for each function. Function \( H \) maps two elements to the same value \( f \), while \( K \) maps each element of \( X \) to different elements of \( Y \).

Transcribed Image Text:a. Is \( H \) one-to-one? Why or why not? Is it onto? Why or why not?
b. Is \( K \) one-to-one? Why or why not? Is it onto? Why or why not?
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