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 $. 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?

Answered: Image /qna-images/answer/cc98372c-104a-4cb6-be89-127ad52ba144.jpg

Answered: {d, e, f, g}. Define 8. Let X = {a, b,…

{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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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

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 $.

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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