3. If |F|q<∞ show: (a) There exists a prime p such that char F = p. (b) q = p some n. (c) a = a for all a € F. (d) If b € K is algebraic over F then b9" = b for some m > 0.

Q: . Prove that for any two nonnegative real numbers, their arithmetic mean is always greater than or…

A:

Q: Suppose you have only 3¢ and 5¢ stamps. (a) Find all values less than 10¢ for which you cannot form…

A: Given:-               Suppose you have only 3¢ and 5¢ stamps. (a) Find all values less than 10¢ for…

Q: 7. For each of the following relations on the set of all real numbers, solve all of the subparts…

A: The problem involves analyzing various relations on the set of real numbers, exploring their…

Q: 4. Let F : A --> B, g : B --> C, and h : B --> C be functions, and suppose that f is onto. Prove or…

A: Given: f:A→B, g:B→C and h:B→C are the functions and f is onto.

Q: 5

A: Step 1: Ascending Property of AN​:For any N1​&lt;N2​, AN1​​ is a subset of AN2​​ since if x∈AN1​​,…

Q: For each of the following identify if the set is finite, countably infinite or uncountable and give…

A:

Q: Use algebra to find the largest possible value of 8 or small- est possible value of N that makes…

A: 23. This equation comes from the ε,δ definition of the limit. As x→2 the function 3x-1→5. So for all…

Q: S is a nonempty set of real numbers that is bounded.

A:

Q: 20. Let the equation │ x – gcd(11111, 111111) │ = gcd(96, 356) – gcd(12, 15), where │ │denotes…

A: To find the integer values of (x) that satisfies the given equation, we first need to calculate the…

Q: How many finite functions exist of the form f: {1, 2, 3,...,m} {1, 2, 3,..., n}? How many of them…

A:

Q: * 30. Let n and k be integers with 1 ≤ k ≤n. Show that n Σ() ( k=1 k n - 1) = (2n+2)/2 - (2n).

A: The answer for the given questions has been solve step by step below please find the attachments…

Q: π Let (x) be the number of prime numbers in the range from 2 to x. Select the pair of inequalities…

A:

Q: Give an example of each or state that the request is impossible. When a request is impossible,…

A: We shall answer the following questions by providing examples or counter statement as appropriate.…

Q: For each statement below decide if it is TRUE or FALSE. • There are two integers n and m such that…

A: We will find out whether the given statements are true or false.

Q: Which of the following function is NOT Q, (n)? А. п —333п? nlgn С. п-1gn D. 219 n E. None Е.

A:

Q: None

A: Step 1: Step 2: Step 3: Step 4:

Q: For each of the following relations on the set of all real numbers, solve all of the subparts on a…

A: Note: “Since you have posted a question with multiple sub parts, we will provide the solution only…

Q: Let S be the set of all positive integers. Define: S -> S by f(1) = 2,  f(2 ) = 3, f(3 ) = 1, and…

A:

Q: None

A: Step 1: Step 2: Step 3: Step 4:

Q: 1.20 Show that, if 0 < |7₂| < |x₁] then, for all n ≥ 1, |T1| |I₁|-|1₂|| n 12 I in-1

A: Given that Let, Now consider geometric series As

Q: (1) Let S be the smallest set of positive integers such that (a) 2 is in S, (b) n is in S whenever…

A:

Q: 6. Let f and g be two arithmetic functions with g(n) = Σan f(d). If g is multiplicative, then so is…

A:

Q: T or F True or not: Every nonempty set of rational numbers that is bounded has a largest number.

A:

Q: 1. True or False? Prove your answer! Suppose A is a countably infinite set of real numbers that is…

A: We know that an open interval does not contain its end point. i.e if (a,b) be any open interval then…

Q: 6. Given the following relations on the set of all integers where (z,y) = R if and only if the…

A:

Q: Let P(x) be given by "x is a prime number," where the domain of x is the set of all positive…

A:

Q: Let X-N(65,36) P(x<70)= O 0.50798 none O 0.98077 O 0.76973

A:

Q: Which of the following sets are countable? ORIN {7,99, 512}. 1 1 1 .}. " 10 100 1000 The set of all…

A: We know R is uncountable and N is coutable.  So, R \ N is uncountable [as R = (R \ N) U N, if R \N…