Please Prove the following, be clear and percise. By removing sets with ever decreasing length, show...

Please Prove the following, be clear and percise.

By removing sets with ever decreasing length, show that we can construct a "Cantor-like" set which has positive length. How large can we make the length of this set?

Expert Solution

Colby Messinger answered 7 months ago

Let A and B be sets. Prove the following please show in as much detail as...

Let A and B be sets. Prove the following please show in as much detail as possible i. A ⊆ B is and only if A U B = B ii. A ⊆ B is and only if A ∩ B = A iii. A ⊆ B is and only if A \ B = empty set

prove that connected sets are preserved by continuous functions. please be clear and do not write...

prove that connected sets are preserved by continuous functions. please be clear and do not write in script

For each of the following sets, prove that thay are convex sets or not. Also graph...

For each of the following sets, prove that thay are convex sets or not. Also graph the sets. a) ? 1= {(?1 , ?2 ): ?1 ^2 + ?2^2 ≥ 1} b)?2 = {(?1 ,?2 ): ?1 ^2 + ?2^ 2 = 1} c)?3 = {(?1 , ?2 ): ?1 ^2 + ?2 ^2 ≥ 1}

Prove the following statements! 1. If A and B are sets then (a) |A ∪ B|...

Prove the following statements! 1. If A and B are sets then (a) |A ∪ B| = |A| + |B| − |A ∩ B| and (b) |A × B| = |A||B|. 2. If the function f : A→B is (a) injective then |A| ≤ |B|. (b) surjective then |A| ≥ |B|. 3. For each part below, there is a function f : R→R that is (a) injective and surjective. (b) injective but not surjective. (c) surjective but not injective. (d)...

[Jordan Measure] Could you prove the following ? Prove that the sets Q ∩ [0, 1]...

[Jordan Measure] Could you prove the following ? Prove that the sets Q ∩ [0, 1] and [0, 1] \ Q are not Jordan measurable.

please show the steps and clear hand writing please show how to Derive the Newton-Raphson formula....

please show the steps and clear hand writing please show how to Derive the Newton-Raphson formula. Diagrams and explanations will be needed.

Numerical MethodsPlease show all steps with clear hand writing. Use numerical methods to Prove that the...

Numerical MethodsPlease show all steps with clear hand writing. Use numerical methods to Prove that the following equations have at leat one solution in the given intervals. (a) x − (ln x)3 = 0, [5, 7] (b) 5x cos(πx) − 2x 2 + 3 = 0, [0, 2]

Give a clear simple argument that each of the following sets is uncountable. a. R ×...

Give a clear simple argument that each of the following sets is uncountable. a. R × Q b. N ∪ P(N) c. P(R) d. (0, π) ∪ {4, 5, 6, 7}

PLEASE SHOW CLEAR CALCULATION PLEASE 1. If a physician deposits $24,000 today into a mutual fund...

PLEASE SHOW CLEAR CALCULATION PLEASE 1. If a physician deposits $24,000 today into a mutual fund that is expected to grow at an annual rate of 8%, what will be the value of this investment: what is the future value factor for each? a. 3 years from now b. 6 years from now c. 9 years from now d. 12 years from now 　 2. The Chief Financial Officer of a hospital needs to determine the present value of $120,000 investment...

For the following two functions prove whether each of the production functions has increasing, decreasing, or...

For the following two functions prove whether each of the production functions has increasing, decreasing, or constant returns to scale. Then find whether the MPL is increasing, decreasing or constant with L. A. ? = ?^1/3?^1/3 B. ? = 3?^3/2

Question