Consider f : X →Y, with domain X = {c,j, v,m, e, s, n, q, u, d, i, g} and codomain Y = {80,08, 57, 97, 82, 74, 39, 84, 01, 35, 15, 94}, as defined below using the set of expressions of the form f(a) = b. It is currently a bijection. Which of the following sequences of operations would cause this function to lose its surjectivity while still remaining a valid injection? f(e) f(g) = 94 f(j) = 08 f(s) = 74 = 57 = 82 f(v) f(m) = 97 = 80 f(c) f(u) = 01 f(d) = 35 f(n) = 39 f(q) = 84 = 15 f(i) Select one: O add 10 to the codomain - remove 80 from the codomain → change the preimage of 94 to d O add k to the domain change the preimage of 84 tom → remove 35 from the codomain O remove 74 from the codomain → remove g from the domain → change the preimage of 15 to d O change the preimage of 01 tod → change the image of j to 82 → change the preimage of 08 to j none of these options O add 37 to the codomain - change the image of d to 37 → removen from the domain O remove d from the domain → change the preimage of 74 to g → add 24 to the codomain

Consider f : X →Y, with domain X = {c,j, v,m, e, s, n, q, u, d, i, g} and codomain Y = {80,08, 57, 97, 82, 74, 39, 84, 01, 35, 15, 94}, as defined below using the set of expressions of the form f(a) = b. It is currently a bijection. Which of the following sequences of operations would cause this function to lose its surjectivity while still remaining a valid injection? f(e) f(g) = 94 f(j) = 08 f(s) = 74 = 57 = 82 f(v) f(m) = 97 = 80 f(c) f(u) = 01 f(d) = 35 f(n) = 39 f(q) = 84 = 15 f(i) Select one: O add 10 to the codomain - remove 80 from the codomain → change the preimage of 94 to d O add k to the domain change the preimage of 84 tom → remove 35 from the codomain O remove 74 from the codomain → remove g from the domain → change the preimage of 15 to d O change the preimage of 01 tod → change the image of j to 82 → change the preimage of 08 to j none of these options O add 37 to the codomain - change the image of d to 37 → removen from the domain O remove d from the domain → change the preimage of 74 to g → add 24 to the codomain

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Similar questions

For function f from {a, b, c, d} to {1, 2, 3, 4, 5}. f(a) = 4, f(b) = 5, f(c) = 1 and f(d) = 3, The set containing the domain has the following elements
Consider f : X →Y, with domain X = {g,c, b, v, h, r, u, s, e, a, n, k} and codomain Y = {54, 73, 92, 74, 42, 61, 30, 14, 41, 27, 71, 45}, as defined below using the set of expressions of the form f(a) = b. Which of the following statements is true? f (b) = 71 f(k) f(s) f(v) f(c) f (g) f(u) f (h) = 92 f(e) f (r) f (n) f (a) = 27 = 41 = 74 42 = 30 = 30 45 = 61 = 73 = 14 Select one: O f(x) is neither an injection nor a surjection O f(x) is a surjection but not an injection O f(x) is an injection but not a surjection O f(x) is not actually a function O none of these options O f(x) is both an injection and a surjection
A = {0, 1, 2, 3, 4} B = {2, 3, 4, 5}Given the sets A and B, how many constants maps are there from A into B.
11 Express the function F(A, B, C)=A+B'C in a sum of minterms form. F(A.B.C) = 2 m(0,2,5,6,7) OF(A,B,C) = Σm(1,2,5,6) OF(A, B, C) = m(1.3,5,6) F(A.B.C) m1,4,5,6,7) he 2
Given g = {(1,c),(2,a),(3,d)}, a function from X = {1,2,3} to Y = {a,b,c,d}, and f = {(a,r),(b,p),(c,δ),(d,r)}, a function from Y to Z = {p, β, r, δ}, write f o g as a set of ordered pairs.
Define L={ <A,B,C>:L(A) is the union of L(B) and L(C)}, where A, B, and C are DFAs. Prove that L is decidable.
2. Consider the given sets A and B. Show a possible bijection for the function f, where f: A-B, and define f for that bijection. a. A= {1, 2, 3, 4, ..., 10} and B = {2, 5, 10, 17, ...,101} •••. 3 b. A= {0, 1}° and B = {1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111}
Answer L1 = {u ∈ Σ∗| u ends with aa}.L2 = {u ∈ Σ∗| u ends and begins with different letters }.L3 = {u ∈ Σ∗| u contains abba}.L4 = {u ∈ Σ∗| u is of the form anbamfor n,m > 0}. Given the above languages:(a) Use the set operators ‘union’ and ‘complement’ to describe L5 = L1 ∩ L2.(b) Prove that L5 is regular.(c) Construct an NFA M that accepts L5, and prove its correctness.?? ?? .
Consider a function f : S→ T defined by f(n) = n², where the domain is the set of consecutive integers S = {-7,..., -2, -1, 0, 1, 2, ..., 7} and the range is the set of consecutive squares T = {-64,...,-9, -4,-1,0, 1, 4, 9, ..., 64}. Which one of the following choices correct describes f? O one-to-one, but NOT onto Oonto, but NOT one-to-one O one-to-one and onto O neither one-to-one nor onto O none of these
L1 = {u ∈ Σ∗| u ends with aa}.L2 = {u ∈ Σ∗| u ends and begins with different letters }.L3 = {u ∈ Σ∗| u contains abba}.L4 = {u ∈ Σ∗| u is of the form anbamfor n,m > 0}. Given the above languages:(a) Use the set operators ‘union’ and ‘complement’ to describe L5 = L1 ∩ L2.(b) Prove that L5 is regular.(c) Construct an NFA M that accepts L5, and prove its correctness.(d) Convert such NFA (from question above) to a DFA using the algorithm from class.(e) Given the DFA you’ve designed in Q3(d), what is δ(s,au), for u ∈ Σ∗. What is δ(s,buaa), foru ∈ Σ∗. Justify your answers. Note that s is the starting state of the given DFA.
A triple (x, y, z) of positive integers is pythagorean if x2 + y2 = z2. Using the functions studied in class, define a function pyth which returns the list of all pythagorean triples whose components are at most a given limit. For example, function call pyth(10) should return [(3, 4, 5), (4, 3, 5), (6, 8, 10), (8, 6, 10)]. [Hint: One way to do this is to construct a list of all triples (use unfold to create a list of integers, and then a for-comprehension to create a list of all triples), and then select the pythagorean ones. def unfold[A, S](z: S)(f: S => Option[(A, S)]): LazyList[A] = f(z) match { case Some((h, s)) => h #:: unfold(s)(f) case None => LazyList() } code in scala
Let A={+,x,a,b}. Show that (a*V ba)+ b is regular over A.