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: WL 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.

Q: 7. i) How many functions are there from the set {1, 2, 3, ...,k} where k is a positive integer, to…

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Q: 7) For each of the following state: a) The type of function 14 Azt 10 10 8 -6-4-2 a 6 4 246 -2 -6 -8…

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Q: Let P(x) be the statement "x^2−x−20⩽0". a. If the domain consists of −4,0,1 and 2, then "∀x,P(x)"…

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A: We have to identify which of the following set is a function.

Q: 1. Let f = {(1, 2), (3, 4), (2, 6), (5, 9}. a) Find the domain of f: {1, 2, 3, 4, 5} O {2, 4, 6, 9}…

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Q: 3. Let A be a finite set. In this exertise functions f, g will be of type g: A → A and ƒ: A → A. (a)…

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Q: How many functions map {1, 2, 3, 4, 5, 6, 7, 8} onto {1, 2, 3, 4, 5} (i.e., how many surjections are…

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Q: 10. Determine whether each of these functions from {a, b, c, d} to itself is one-to-one. a) f(a) =…

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Q: ? ? ? Hint: ✰✰✰✰✰✰✰.. 5. {(b, 6), (h, 2), (0, 6), (r, 4), (s, 27)} 6. {(b, 2), (h, 27), (0, 4), (r,…

A: For the given set , does it define function f:X--&gt;Y .

Q: Function f: {a,b)³ → (a,b) is defined by the following rule. For strings € (a,b)³, f(s) = f(x1x2x3)…

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Q: Consider the set M = {0, 2, 4, 6} and N = {1, 3, 5, 7}. Determine if each of the following ordered…

A: According to guideline we need to solve first 3 subparts.

Q: F (8)

A: We are given setsWe have to answer (d), (e), (f) and (g).

Q: 2. Let N = {1,2,3,...}. Are the following functions injective, surjective and/or bijec- tive? (i) f:…

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Q: Given F(A, B, C, D) = A'B'C'D' + A'B'C'D + A'BCD' + A'BCD, express F(A,B,C,D) and F '(A,B,C,D) in…

A: Solution: Given that F(A, B, C, D) = A'B'C'D' + A'B'C'D + A'BCD' + A'BCD Now, truth table Row no.…

Q: A.How many functions are there from set A with 4 elements to set B with 6 elements? B.How many…

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Q: A = {5,6} B = {5, 7 ,8} S = {n | n >= 3 is an odd integer} A relation R from AxB to S is defined…

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Q: 5. Let D = {1, 2, 3, 4, 5}, C = {a, b, c, d}, and g = {(1,a), (2,c), (3,d), (4,c)}. Determine…

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Q: Given a finite set S, find all possible values of |S] so that the set {(a, b) | (a E S) A (b e S) ^…

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Q: 5. For example, fuzzy sets A and B are defined by the function : for 2 ≤x≤ 10 A(x) = 1-(|x-61/4) 0…

A: As per the question we are given two fuzzy logic sets A(x), B(x) and from that we have to find: The…

Q: 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…

A: S be the set of all strings of a's and b's of length 3 . Then to find f(aaa) , f(aab) , list all the…

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Q: Question (2) 으 (2-3)" P(군)= Let then : %3D a Determine Zo=? and ana? b) Determine the Covergance…

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Q: How many injective functions have domain [10], codomain [10] and are not surjective?

A: Ans : 0 (zero)

Q: Let A={1, 2, 3, 4, 5} and B={a, e, i, o, u}. If ƒ: B → A is a function defined by f ={(a, 4), (u,…

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Q: w many different functions are there from a set with 10 elements to sets with 2 elements?

A: product rule : If one event can occur in m ways and a second event can occur in n ways ,the number…

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A: Answer given below.

Q: 6. (a) Let sets S = {A, B} × {1, 2, 3} and T = {A, B} × {1, 2, 3, 4} . How many different one %3| to…

A: The total number of elment in set s will be  and total number of element in set T will be

Q: What is the domain of the following: {(3,4), (9, 1), (10, 5), (2, 15), (8, 4)} O {3, 4,9, 1, 10, 5,…

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Q: Let F(x.y): "x is friend with y", N(x): "x is funny", W(x): "x is wise", R(x): "x is fair". The…

A: Given: The functions Fx,y: "x is friend with y". Nx: "x is funny". Wx: "x is wise". Rx: "x is…

Q: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} onto {1, 2, 3} (i

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Q: Find a function from the set {1,2,.....30} to {1,2,.....10} that is a 3-to-one correspondence.

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Q: 3. Let A be a finite set. In this exertise functions f, g will be of type g: A →A and f: A → A. (a)…

A: Injective and surjective function