A Function on a Set of StringsLet S be the set of all strings of a's and b's of length 4. Let B = {0, 1}Let f:S → B be defined as follows:fleS1 if s has an a in the rightmost placef(s)-0 if s does not have an a in the rightmost placeEvaluate the following:a) f(aaaa)b) f(abbb) =c) f(abab) =d) f(bbba) =%3|e)List all of the ordered pairs for which f(s) = 1.

Answered: Image /qna-images/answer/4f7718a3-26a9-44c6-a9cb-d3f92e3b4463.jpg

Answered: Let S be the set of all strings of a's…

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 A = {a, b, c, d, and let R be the relation R = {(a, a), (b, b), (c, c), (d, d), (c, b), (a, d), (b, a), (b, d), (c, d), (c, a)}. Is R a total order on A? Yes No Justify your answer. (Select all that apply.) R is antisymmetric. R is not antisymmetric. There exists a chain in R that contains every element of A. There does not exist a chain in R that contains every element of A. R is transitive. R is not transitive. Each element of A exists in R. Each element of A does not exist in R. R is reflexive. R is not reflexive.
Let A = {1,3} and B = {2,4}. (a) Draw a picture of the set A × B. (b) Compute P(A × B).
Which of the following operations on the set Z has more than one left neutral element and no right neutral element? (a) a ° b = b - a (b) a°b = b (c) a°b = a + ab - 1 (d) a°b = ab (e) Such a prescription does not exist.
7. Let A and B be sets, and let f: A → B and g: B –→ A be functions. Suppose that: • go f(a) = a for every a E A; fo g(b) : = b for every b E B. Prove that f is bijective.
In N × N clause β for (a,b), (c,d) ∈ N × N defined as:(a,b)β(c,d) = ad = bcExamine the properties of the relation β.
Determine whether each of these functions f:Z->Z is one-to-one, on-to, one-to-one correspondence, respectively. a) f(n) = n-1 b) fln)= n² +1 c) f(n)= n² d) fir) = [n/2]
Let f(a, b) = (a + b+ 2) + (2a + 4b + 6)x + (a +b+c)æ² and set F = {f(a, b) : a, b € R}. What is the value of c if f(1,0) + f(0,1) e F? 6 3 O 1 4.
Which of the following operations on the set Z has more than one left neutral element and at least one right neutral element? (a) a°b = b - a (b) a°b = b (c) a°b = a + ab - 1 (d) a ° b = ab (e) Such prescription does not exist.
d) Draw an arrow diagram of the inverse for the bijection function found in (c). Define W:Z → Z and V: Z → Z by the rules W(a) = a? and V (a) = a mod 5 for all integers a. Find the following: e) (W • V)(6) (V • W)(9) iii. i. ii. Is (W • V) = (V •W) for all integers a e Z? Justify your answer. -1-
Let X = {a,b,c} and Y = {1,2,3,4}. Which of the relations A,B,C defined below are functions from X to Y? a.) A = {(a,1), (b,2), (c,3)}
List all the ordered pairs in the relation R = {(a, b)| gcd(a,b) = 1} on the set {2, 3, 4, 5, 6}.
Find n(A) for the set A. A = {1, 1, 2, 2, ..., 5, 5} O n(A) = 10 n(A) = 6 O n(A) = 5 n(A) = 3

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