1. Let A= {x, y, z} (a) If possible, give an example of a subset of P(A) with cardinality 4. (b) If possible, give an example of a element of P(A) with cardinality 4. (c) Does there exist a function f :A-P(A) which is 1- 1? If such function exist give an example, if no such function exists, explain why.

Q: 7. (10 points) Let f: A B be onto. Prove that S((C)) = C for all sets CC B.

A:

Q: 1. If f is a function on a set A = {1,2,3,4,5} such that f = {(1,2), (2,3), (3,4), (4, x), (5,5)}.…

A: Answer C

Q: he following function: =: Find fxy. f(x, y) = 5x4y6x4y5 - 21

A:

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

A:

Q: (b) Let A = {x € R | 0 < x < 1} and B = {x € R | 0 < x < 2} . Determine whether A and B have the…

A:

Q: Suppose f function between infinite sets A and B, f is not onto function, does the sets A and B have…

A: Yes. It is possible that A and B have same cardinality. Let A and B both are the set of natural…

Q: Show that the two intervals (0, 1) and (0, 2) have the same cardinality.

A: In mathematics, cardinality is a measure of the "size" of a set, which can be defined as the number…

Q: Let f : N → P(N) be the function defined by f(n) = {n, n + 1, . . . , 2n} The following statement is…

A: 1) is false and 2) is true.

Q: Theorem 9. The following statements regarding the set E are equivalent: (i) E is measurable. (ii)…

A:

Q: How to show that |Z+| (that is, the cardinality of Z+) is not equal to |(0,1)| (cardinality of the…

A:

Q: ›) Prove that if the function ƒ is 1-1, then ƒ−¹ is a function. Caution! The ONLY assumptions here…

A: We use definition of function and one-one function to prove that f-1 is function.

Q: Suppose that f : A → B is a function, viewed as a relation (set of ordered pairs). Let f* denote the…

A:

Q: 20 - If f is a function on a set A= {1,2,3,4,5} such that f= { (1,2), (2,3), (3,4), (4,x), (5,5)}.…

A: Use the property that in bijective functions each element of doamin and codomain has image and pre…

Q: Show that the function f: [1, 2] → [1,8], f(x) = 7x - 6 is a bijection. What relationship exists…

A:

Q: A = { 3, 0, 1 } B = { y, x }  what is the cardinality of A x P(B) ?

A: Given that, A = {3,0,1}  B ={ y , x }  Power set of B = {{},{x},{y},{x,y}}  Generally cardinality is…

Q: Let A = {1, 3, 5, 7, 9, 11}, B= {a, b, c, d, e}, and ƒ be the function from A to B defined as below:…

A:

Q: 6. Show that (an)neN C R is bounded if and only if lim supn→∞ an < +∞o.

A: To Prove:  ann is bounded sequence if and only if limsupan&lt;+∞.

Q: Let The the domain of f is the set of all real numbers except Number Moreover, f (2) f(t+1) = Number…

A:

Q: A function F from a set A to a set B is a relation with domain A and co-domain B that satisfies the…

A: Relation: Let A  and B  be two sets then relation between A nd B means  the collection of the…

Q: c) Describe the set of all 7. For a function f:A → B, the statement "f is surjective" is defined by…

A:

Q: We have the set of all functions from R to R (f(R,R)). How do I prove that this function's…

A: Kindly refer to Step 2 for the solution.

Q: I z2+ 8z + 12 f(z) = a) Give the domain of f (in interval notation) b) Find the critical numbers of…

A: Disclaimer: “Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Prove that {2, 3, 4, ...} is countably infinite. You must prove that your function is bijective

A:

Q: 6. Let 2 be a set and f, g: → R. Assume max{f(x) + g(x) | x = }, max{f(x) |x€N}, and max{g(x) | x =…

A:

Q: 8) a) List the elements of each of the following sets, using the .' notation where necessary: i)…

A: Since it is multiple questions with multipart. As per our company guidelines, we have to solve the…

Q: Justify rigorously the given set is open in R³. (a) A = {(x, y, z) |x>0, y 9}. (b) B = {(x, y, z) |…

A:

Q: For a set A, let {0,1} A be the set of all functions from A to the two point set {0,1}. Prove that…

A:

Q: (a) What is the cardinality of the interval (0, 1), finite, countably infinite, or uncountable? (b)…

A:

Q: For every element r in A, there is an element y in B such that (x, y) is in F. Can you please…

A: Relation: The relation from a set A to a set B is a subset of Cartesian product A×B. Function: The…

Q: the book is "First Course on Fuzzy Theory and Applications"

A: To show: The given function satisfies the condition

Q: 13. (9 points) Let D be the set of finite subsets of positive integers. Let S be the set of all…

A: The objective of this question is to find the set of all even factors of given numbers using the…

Q: --to-one o? [ Se

A:

Q: Show that any open interval (a,b) of the real numbers has the same cardinality as (0,1). (note that…

A:

Q: Which of these relations on the set of all functions from ℤ to ℤ are equivalence relations?…

A: (a) R = {(f, g) | f (1) = g(1)}        Now, as f(1) = f(1), thus (f, f) ∈ R.              Hence, R…

Q: Define the function f: R → R by f(x) To prove that f is onto, we need the following: = x³ +7 \x € R.…

A:

Q: Determine whether the function f from { a, b, c, d} to { a, b, c, d} is injective (one - to - one),…

A:

Q: (a) What is the cardinality of the interval (0, 1), finite, countably infinite, or uncountable? (b)…

A: Schroder-Bernstein Theorem: If there exists injective functions f : A→B and g : B→A between the sets…

Q: example of a function from R in R for which f (A) = B for all A and B open sets in R, but which is…

A:

Q: Let P(x) = (x - 1)(x - 2)² (x-3)³. Find the set of r such that x (a) P(x) = 0, (b) P(x) 0.

A:

Q: (n) Find the domain of fog in terms of the domain of f and g as a preimage. (0) Show, if A is any…

A:

Q: let A = { 1, 2, 3, 4, 5} and B = { a, b, c, d, e, f}. in each case, give an example of a function f…

A: