Question

In: Advanced Math

Please justify and prove each statement (Use explicitly the four axioms) a) Prove that a finite...

Please justify and prove each statement (Use explicitly the four axioms)

a) Prove that a finite positive linear combination of metrics is a metric (Use explicitly the four axioms). If it is infinite, will it be metric?

b) Is the difference between two metrics a metric? (d1 - d2)

Solutions

Expert Solution


Related Solutions

Assume B is a Boolean Algebra. Prove the following statement using only the axioms for a...
Assume B is a Boolean Algebra. Prove the following statement using only the axioms for a Boolean Algebra properties of a Boolean Algebra. Uniqueness of 0: There is only one element of B that is an identity for + please include all the steps.
Use models to show that each of the following statements is independent of the axioms of...
Use models to show that each of the following statements is independent of the axioms of incidence geometry: (a) Given any line, there are at least two distinct points that do not lie on it. (b) Given any point, there are at least three distinct lines that contain it. (c) Given any two distinct points, there is at least one line that does not contain either of them.
Prove that if a finite group G has a unique subgroup of order m for each...
Prove that if a finite group G has a unique subgroup of order m for each divisor m of the order n of G then G is cyclic.
5. For each set below, say whether it is finite, countably infinite, or uncountable. Justify your...
5. For each set below, say whether it is finite, countably infinite, or uncountable. Justify your answer in each case, giving a brief reason rather than an actual proof. a. The points along the circumference of a unit circle. (Uncountable because across the unit circle because points are one-to-one correspondence to real numbers) so they are uncountable b. The carbon atoms in a single page of the textbook. ("Finite", since we are able to count the number of atoms in...
Indicate whether each statement is True or False. Briefly justify your answers ( Please answer C...
Indicate whether each statement is True or False. Briefly justify your answers ( Please answer C and E both ) (c) The set of all 3 × 3 matrices A with zero trace (T r(A) = 0) is a vector space under the usual matrix operations of addition and scalar multiplication. ( e) If x⃗1 and x⃗2 are in the null space of a square matrix A, then any linear combination of x⃗1 and x⃗2 is also in the null...
Ex 1. Prove by contrapositive the following claims (please, write down the contrapositive for each statement...
Ex 1. Prove by contrapositive the following claims (please, write down the contrapositive for each statement first). Claim 1: Let n be an integer. If n 2 − 6n + 5 is even, then n is odd. Claim 2: Let a, b, c be positive real numbers. If ab = c then a ≤ √ c or b ≤ √ c.
Please prove this and explain each step. Thank you. Use logical reasoning to solve the following...
Please prove this and explain each step. Thank you. Use logical reasoning to solve the following puzzle: Five friends disagree on whether to play video games or basketball. Either Alice or Bob, or both, want to play video games. Cindy and Don disagree on what they want to play. If Ellen plays video games, then so does Cindy. Alice and Don will play the same game. If Bob plays video games, then so do Alice and Ellen. Who is playing...
Determine whether each statement is true or false. If it is true, prove it. If it...
Determine whether each statement is true or false. If it is true, prove it. If it is false, give a counterexample. a) For every function f : X → Y and all A ⊆ X, we have f^−1 [f[A]] = A. (b) For every function f : X → Y and all A ⊆ X, we have f[X \ A] = Y \ f[A]. (c) For every function f : X → Y and all A, B ⊆ Y ,...
For each problem identify the sampling distribution explicitly using the Central Limit Theorem, use probability notation...
For each problem identify the sampling distribution explicitly using the Central Limit Theorem, use probability notation to indicate what you are being asked to find, find your probabilities showing all your work, including diagrams. Interpret your final results. Submit your completed homework to Canvas. A 2012 survey of adults 18 years and older reported that 34% have texted while driving. A random sample of 125 adults was selected.    What is the probability that 36 or more people in this...
In each case below either prove that the statement is True or disprove it by giving...
In each case below either prove that the statement is True or disprove it by giving an example showing that it is False. (i) If B is a fixed 2 × 2 matrix, then the set U = {A|A ∈ M22, AB = 0} is a subspace of M22. T or F (ii) If u, v, w are vectors in a vector space V , then span {u, v, w} = span {u + v, u + w, v +...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT