Theorem 2. Suppose u e F where F is an ordered field. Then u is positive f and only if u > 0. Similarly, u is negative if and only if u < 0.

Q: Prove the following fact: A" = 3"-1A. 1 1 1 1 1 1 1 1 1 A =

A: Given, A =111111111  We have to  prove An = 3n-1A

Q: 0 -1 0] If R =|1 2-1, then R-1= 1 1 0

A: Matrix is a mathematical object containing numbers arranged in rows and columns. The order of a…

Q: Trail 1 Trail 3 -H- H-- Trail 4 Trail 2 A park has a system of trails for walking and biking. Trail…

A:

Q: Determine the positive real numbers x and y such that • x + y = 4 and 2.n2 + y² is small as…

A:

Q: Consider the statement Vxy (y <x) Let x be all natural numbers Let y = x-1 Is the statement true or…

A: We know that the set of natural numbers starts from 1 and it is an infinite set. This set is…

Q: (2c) Prove or disprove the following statement: “ A UBCANB for any A and B "

A:

Q: (B1>0 (g) If a > b and c> d, then a + c > b + d. h) If a > b> 0 and c > d > 0, then ac > bd. i) If a…

A: For (f) ,We use a theorem that "if n∈ℤ and n≠0 then n2&gt;0.

Q: 1. Let X be the set of real numbers with the usual pseudometric. Find the derived set and the…

A:

Q: 9. Prove the following algebraic identity: (a - b)(a? + ab +b?)=a' -b'

A:

Q: 2. For all sets X, Y and Z, determine whether each of the statement is true or false. If it is true,…

A: (a) False. We know that if a set A has cardinality n , then it's power set P(A) has cardinality 2n…

Q: 3. Prove the pythagorean Theorem

A:

Q: Prove than any pair of elements in H can be mapped to the positive y-axis by an element of SL(2, R).

A: According to the given information, it is required to prove that any pair of elements in H can be…

Q: How many different size of infinity are there? How does it relate to one-to-one correspondence?

A: There are actually many different sizes or levels of infinity; some infinite sets are vastly larger…

Q: Prove bey wnduc hiou that for n22.

A:

Q: 1. Choose one of the forms of the FAC (the fundamental approximation of calculus) and an application…

A: FIRST FUNDAMENTAL THEOREM OF CALCULUS The first fundamental theorem of calculus states that, if f is…

Q: Suppose that x is a real number and that UCR. Prove that the following two conditions are…

A:

Q: (2b) Let A and B be sets. Prove that A – B is disjoint from A n BC LA O BE

A: The set A∩B is defined as A∩B=x|x∈A and x∈B The set A-B is defined as A-B=x|x∈A and x∉B Two sets are…

Q: -2 1 2 -1 1 -1 2. LetA= Then find A-1 if it exist. 1

A:

Q: From fundamental property relations, proof the following equation is valid. %D | T.

A:

Q: Find all the values of z for which 1+z 1 1 1 1 1+z 1 1 1 1 1+z 1 1 1 1 1+z <= 0.

A:

Q: Let 4 1 - 3 -2 -9 and 1 A =| - 3 В C =| 0 3 Prove that 5 - 2 -1 1 1 – 4 | (BA)" – A" B" + AC = AC,…

A: (BA)T - ATBT + AC = AC In LHS, We know that, By the properties of Transpose, (BA)T = ATBT .…

Q: 1. Prove that fraction where m is z-4

A: Given: zn-1z-1 ⇒zn-1nz-1 ----(1) Let apply the limit in equation (1) limz→1zn-1nz-1 ----(2) Let n=pq…

Q: MA Let r [-1. 1] and F(x) = f, f(t)dt. where the function f is defined by 1. if x > 0. f(x) = { 0.…

A: f is not continuous at x=0.

Q: Prove or disprove: If (xn) and (yn) are subsequences of each other, then xn = yn.

A: Definition: Suppose ann∈ℕ be a sequence. A subsequence of this sequence is a sequence of the form…

Q: Question 1. (a) Prove that for z, w = C, Re (zw) = |z||w| if and only if z = sw for some positive…

A: a)  suppose that the complex numbers are   z=a+ib and w=c+id .  Then we see that w¯= c-id  we see…