For each of the following functions, determine whether the function is: Injective (one-to-one). Surjective (onto). ⚫ Bijective. Justify your answers. 1.3 f: R→ ZZ such that f(x) = [4x] (i.e., ceiling of 4x).
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- Q. Let A = {a, b, c, d, e} and B = {1, 2, 3, 4, 5, 6, 7, 8}. How many functions f : A → B(a) ... are injective?(b) ... are not injective?(c) ... are such that f(a) = f(b) = f(c)?(d) ... are such that exactly three elements of A have 8 as an image?(e) ... are surjective?Answer the 2 questions, will upvote if complete, short solution/explanation will dopls do not reject. thanksFor all a and b in the domain of a function f, the function is injective iff f(a) #f(b) a=Db f(a)=f(b) a=b f(a)=f(b) atb o fly)=x iff f(x)=y A Moving to another question will save this response. 5
- Choose all that apply: 1. For the functions, n", and c", what is the asymptotic relationship between these functions? Assume that k >= 1 and c > 1 are constants. a. nk is O(c") b. nk is N(c") c. nk is 0(c") 2. For the functions, Ign and logan what is the asymptotic relationship between these functions? a. Ign is O( logsn) b. Ign is N( logsn) c. Ign is 0( logsn)Answer the following multiple choice questions: - If B represented the set of Boolean values true and false, then the set of Boolean functions B x B → B is... A) finite B) uncountably infinite C) countably infinite - The set of functions from {0,1} to N is... A) finite B) uncountably infinite C) countably infinite - The set of functions from N to {0,1} is... A) finite B) uncountably infinite C) countably infiniteDetermine the truth value of each of the following statements if the domain consists of all integers. If it is true, find a different domain for which it is false. If it is false, find a different domain for which it is true. Justify your answer. EXAMPLE: Vx (x ≤2x) Answer: False. If x=-1, then 2x = -2 and -1 > -2. True when the domain consists of all nonnegative integers x, x ≤2x. (a) Vr ((x+2) is even) (b) x (264) (c) VbVx (b² has a maximum value of 256) (d) x ([x/2x/2] = 0) (e) Vx ([x/2][2/2] = 1)
- So would this be a disprove, i.e. there is no such function?Write a function solver that takes a non-negative integer upper_bound as an argument, and prints all non-negative integers i line-by-line in ascending order such that i is at most upper_bound, and i+100 and i+268 are perfect squares. Note that the function solver prints the numbers instead of returning them, but you may want to define a helper function is_perfect_square to return whether a number is a perfect square.Consider a function: f (n) = n – 1. What function is it. Select one: a. onto b. one to one c. not a valid function d. Bijective CLEAR MY CHOICE O O O
- The following function f is Z-→ Z: f(x) = -x2 + 998 %3! Which of the following are true? (There may be multiple answers) fis not Onto and not One-to-One. f is not a function. Ofis Onto. M fis One-to-One.* .Determine whether the function f: Z × Z →Z is onto if f (m, n) = m + n onto one to one O not one to one and not onto OFor each of the following statements, let the domain be all animals in the world. 1. Express each of the statements using quantifiers and propositional functions. 2. Form the negation of the statement so that no negation is to the left of the quantifier. 3. Express the negation in simple English. (Do not simply use the words “it is not the case that..."). (a) All dogs have fleas (b) There is a horse that can add. (c) Every koala can climb. (d)No monkey can speak French. (e) There exists a pig that can swim and catch fish.