1. (1 pints) Let A = {a,b,..., z} and B = {1,2,..., 10} and define f = {(c, 6), (b, 9), (b, 8), (d, 10), (c, 10), (a, 1)} (a) Is f a relation from A to B? Why or why not? viw nisiqes yn (s) odzo jon at ydw nielqus ylsind (d) lons are there from A to B Pri (b) Explain why f is not a function from A to B.
1. (1 pints) Let A = {a,b,..., z} and B = {1,2,..., 10} and define f = {(c, 6), (b, 9), (b, 8), (d, 10), (c, 10), (a, 1)} (a) Is f a relation from A to B? Why or why not? viw nisiqes yn (s) odzo jon at ydw nielqus ylsind (d) lons are there from A to B Pri (b) Explain why f is not a function from A to B.
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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![**Question 1:**
Let \( A = \{a, b, \ldots, z\} \) and \( B = \{1, 2, \ldots, 10\} \) and define
\[ f = \{ (c, 6), (b, 9), (b, 8), (d, 10), (c, 10), (a, 1) \} \]
(a) **Is \( f \) a relation from \( A \) to \( B \)? Why or why not?**
A relation from \( A \) to \( B \) is a set of ordered pairs where the first element of each pair is from set \( A \) and the second element is from set \( B \). The set \( f \) given is a collection of such ordered pairs, thus (a) Yes, \( f \) is a relation from \( A \) to \( B \).
(b) **Explain why \( f \) is not a function from \( A \) to \( B \).**
A function from \( A \) to \( B \) is a relation where each element in \( A \) is related to exactly one element in \( B \). In the set \( f \), the element \( b \) from set \( A \) is related to two different elements in set \( B \) (both 8 and 9), as is the element \( c \) (both 6 and 10). Therefore, (b) \( f \) is not a function from \( A \) to \( B \) because an element from \( A \) has more than one association with elements in \( B \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80eba1b3-8d69-40f7-985c-31697cc21abc%2F99bd41e1-bc55-4aa7-b763-5167c6420657%2Fvo2zgcg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 1:**
Let \( A = \{a, b, \ldots, z\} \) and \( B = \{1, 2, \ldots, 10\} \) and define
\[ f = \{ (c, 6), (b, 9), (b, 8), (d, 10), (c, 10), (a, 1) \} \]
(a) **Is \( f \) a relation from \( A \) to \( B \)? Why or why not?**
A relation from \( A \) to \( B \) is a set of ordered pairs where the first element of each pair is from set \( A \) and the second element is from set \( B \). The set \( f \) given is a collection of such ordered pairs, thus (a) Yes, \( f \) is a relation from \( A \) to \( B \).
(b) **Explain why \( f \) is not a function from \( A \) to \( B \).**
A function from \( A \) to \( B \) is a relation where each element in \( A \) is related to exactly one element in \( B \). In the set \( f \), the element \( b \) from set \( A \) is related to two different elements in set \( B \) (both 8 and 9), as is the element \( c \) (both 6 and 10). Therefore, (b) \( f \) is not a function from \( A \) to \( B \) because an element from \( A \) has more than one association with elements in \( B \).
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