TutorMe homepage

SIGN IN

Start Free Trial

Justin M.

Student at UNC-CH

Tutor Satisfaction Guarantee

Set Theory

TutorMe

Question:

Write out the set P(P(P(∅))) where P() represents the power set.

Justin M.

Answer:

∅ = {}, P(∅) = {∅} P(P(∅)) = {∅,{∅}} P(P(P(∅))) = {∅,{∅},{{∅}},{∅,{∅}}}

Discrete Math

TutorMe

Question:

Consider the sequence of integers a_n defined by a_1=1 and for n>=2, a_n = 2a_{n-1} +1. Find the simplest possible formula for a_n and prove your answer using induction.

Justin M.

Answer:

The sequence starts out 1 3 7 15 31. We can recognize that this sequence is the sequence of Mersenne numbers that are generated by the function a_n = 2^n-1. Now let us prove the base case, P(1) = 2^1-1 = 1 = a_1. Let assume that for all k a_k = 2^k-1 holds. Now let us look at a_{k+1} = 2a_k+1. Since a_k =2^k-1 we see that a_{k+1} = 2(2^k-1)+1 by the inductive hypothesis. 2(2^k-1)+1 = 2^{k+1} -1. Thus by the principle of mathematical induction we have shown that a_n = 2^n -1 for all n.

Computer Science (General)

TutorMe

Question:

Given a binary search tree what information would be needed on each node to find the kth element in O(log(n))?

Justin M.

Answer:

On each node you would need to have the number of nodes that are under that node. As well as the regular information needed for a binary search tree such as the node to the left and right.

Send a message explaining your

needs and Justin will reply soon.

needs and Justin will reply soon.

Contact Justin

Ready now? Request a lesson.

Start Session

FAQs

What is a lesson?

A lesson is virtual lesson space on our platform where you and a tutor can communicate.
You'll have the option to communicate using video/audio as well as text chat.
You can also upload documents, edit papers in real time and use our cutting-edge virtual whiteboard.

How do I begin a lesson?

If the tutor is currently online, you can click the "Start Session" button above.
If they are offline, you can always send them a message to schedule a lesson.

Who are TutorMe tutors?

Many of our tutors are current college students or recent graduates of top-tier universities
like MIT, Harvard and USC.
TutorMe has thousands of top-quality tutors available to work with you.

Made in California

© 2019 TutorMe.com, Inc.