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…

A:

Q: On the set A = {a, b, c, d, e, f, g, h} is given by the relation R = {(a; b), (a; c), (a; d), (a;…

A: The set is A=a, b, c, d, e, f, g, h and the relation is R=a; b, a; c, a; d, a; e, b; f, c; f, d; g,…

Q: 3. Let a, b, c, d be real numbers with a < b and c < d. Find a one-to-one correspondence between (a,…

A:

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)"…

A: Given: Here is the given statements, 1. Px=x2−x−20≤0 To find: Is it true or false that "∀x,P(x)" is…

Q: . How many Boolean functions are there of degree 7? Explain.

A:

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}…

A:

Q: How many one-to-one functions are there from a set with m elements to a set with n elements, where…

A:

Q: Let S = (1, 2, 3, 4). With respect to the lexicographic order based on the usual less than relation,…

A:

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)…

A:

Q: Given the function f= {(n,n²)such thatn< 3,n€N} as a set of ordered pairs in set-builder notation,…

A:

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)…

A:

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: 6. Consider these functions from the set of students in a discrete mathematics class. Under what…

A: (a) The students from the set of student if it is assigned to his/ her mobile number is one to one…

Q: Write each of the following sets using a defining property (Ax- iom of Specification) and using a…

A:

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) ^…

A:

Q: 9.4. Let A = {a, b, c} and B = {1,2,3,4}. Then R1 = {(a, 2) , (a, 3) , (b, 1),(b,3), (c, 4)} is a…

A:

Q: O Recall that the gradient of a scalar field f can be expressed in spherical polar basis as + e af…

A:

Q: Let N={1,2,3,4,...}. Let P(x,y) be the predicate that x is less than or equal to y^2

A: (d) S = {1, 2, 3, 4, 5, 6, 7, 8, 9} (e) T = {3,4,5,6,......} (f) R = {} (empty set)Explanation:(d)…

Q: 2. A- (x|x2-2) 8- (x|x< 6) (a) A nc (b) A nB

A: Sets