4. Let W be the set of all words in the English language and let L be the set of letters{A, B, C,...,Z}. Let f: W→→L be the function that takes as input a word w and out-puts the first letter of the word.(a) Compute f({APPLE, CHERRY, STRAWBERRY}).(b) Give three elements in the set f-¹(P).(c) Is f a bijection? Use one or two sentences to explain your answer.

Answered: Image /qna-images/answer/291c0305-39a7-4ae2-ae37-697b36b96872.jpg

Answered: 4. Let W be the set of all words in the…

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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Let S be the set of all strings of a's and b's of length 3. Let B = {0, 1}. Let f: S B be defined as follows. S1 f(s) 0if s does not contain the letter "b" 1 if s contains the letter "b" Evaluate the following: a) f(aaa) b) f(aab) c) List all the ordered pairs for which f(s) = 1 .
w many different functions are there from a set with 10 elements to sets with 2 elements?
16 6 24 8 32 10 40 A) function domain:{16, 24, 32, 40) range: (4, 6, 8, 10} B) function domain: (4, 6, 8, 10} ) not a function range: (16, 24, 32, 40) A) A is correct. B. B is correct. C is correct. ttt1
How many functions map {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} onto {1,2,3} (i.e., how many surjections are there)?
b. Which sets are functions?• (1, 2) (2, 3) (3, 4) Yes/No If no, why• (1, 2), (2, 3) (2, 5) Yes/No If no, why• (States, senators) Yes/No If no, why• (Birthdays, People born that day) Yes/No If no, why• (States, Number of senators) Yes/No If no, why
3. Suppose that we have the following four tuples in a relation S with three attributes ABC: (1,2,3), (4,2,3), (5,3,3), (5,3,4). Which of the following functional (-->) and multivalued (-->>) dependencies can you infer does not hold over relation S? a) A-->B b) A-->>B c) BC-->A d) BC-->>A e) B->C f) B-->>C
9.25. Let A = {1, 2, 3, 4, 5, 6}. The relation R = {(1,1), (1, 5), (2, 2), (2, 3), (2, 6), (3, 2), (3, 3), (3, 6), (4, 4), (5, 1), (5, 5), (6, 2), (6, 3), (6, 6)} is an equivalence relation on A. Determine the distinct equivalence classes.
Let f {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} → {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} be defined by f(x) = 2x if x 6. Select all the elements of f({5,6}). 01 3 2 4 Select all the elements of f-¹({5,6}). 3 04 Select all the elements of ƒ−¹(ƒ({5,6})). 3 04 2 Select all the elements of ƒ(ƒ¯¹({5,6})). 01 3 04 5 5 06 6 07 07 07 07 U O 8 8 8 8 9 9 9 ✔10 10 10 10
This question confuses me, I dont get what is being asked? How do I approach this? "Let A be a nonempty set and let B be a subset of the power set P(A) of A. Define a relation R from A to B byxRY if x ∈ Y. Give an example of two sets A and B that illustrate this. What is R for these two sets?"

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