Question

Prove that if there are n≥2 people at a party, then at least 2 of them...

Prove that if there are n≥2 people at a party, then at least 2 of them have the same number of

friends at the party.

(Hint: The Pigeonhole Principle states that if n items are placed inmcontainers, wheren>m, at

least one container must contain more than one item. You may use this without proof.)

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
John has n acquaintances. He wants to meet 3 of them every day of 2018 for...
John has n acquaintances. He wants to meet 3 of them every day of 2018 for coffee at his home. What is the smallest value of n such that he can do this without calling the same set of three people more than once during 2018? Note that a person can come on multiple days, but never more than once with the same 2 other people. For the above n, we want to make a statement like “There is some...
Pigeonhole 1. If 13 people in one room, show that at least 2 people born in...
Pigeonhole 1. If 13 people in one room, show that at least 2 people born in the same month. 2. Show that if 7 numbers was chosen from 1 to 12, any 2 of it will add to 13. 3. How many friend you should have to ensure that at least 5 of them have the same birth month? 4. 6 persons collect their money and the amount is RM 21.61. Show that at least one of them must have...
1/ Imagine a party with n people. When a person comes to the party they go...
1/ Imagine a party with n people. When a person comes to the party they go and shake hands with a few other people (but not necessarily everyone - in fact there can be unfriendly people who do not shake hands with anyone!). None of the attendees narcissistic enough to shake hands with themselves. Prove that there are two people who shake the same number of hands. For example, suppose 3 people attend the party and everyone shakes hand with...
Prove the following theorem: For every integer n, there is an even integer k such that...
Prove the following theorem: For every integer n, there is an even integer k such that n ≤ k+1 < n + 2. Your proof must be succinct and cannot contain more than 60 words, with equations or inequalities counting as one word. Type your proof into the answer box. If you need to use the less than or equal symbol, you can type it as <= or ≤, but the proof can be completed without it.
Prove the following theorem: For every integer n, there is an even integer k such that...
Prove the following theorem: For every integer n, there is an even integer k such that n ≤ k+1 < n + 2. Your proof must be succinct and cannot contain more than 60 words, with equations or inequalities counting as one word. Type your proof into the answer box. If you need to use the less than or equal symbol, you can type it as <= or ≤, but the proof can be completed without it.
Prove that there is no positive integer n so that 25 < n^2 < 36. Prove...
Prove that there is no positive integer n so that 25 < n^2 < 36. Prove this by directly proving the negation.Your proof must only use integers, inequalities and elementary logic. You may use that inequalities are preserved by adding a number on both sides,or by multiplying both sides by a positive number. You cannot use the square root function. Do not write a proof by contradiction.
For n > 2, suppose that there are n people at a party and each of...
For n > 2, suppose that there are n people at a party and each of these people shake hands (exactly one time) with all of the other there (and no one shakes hands with himself or herself). Find the total number of hand shakes by solving a non-homogeneous recurrence relation.
fifty-one numbers are chosen from 1-100 prove that at least 2 of them are consecutive
fifty-one numbers are chosen from 1-100 prove that at least 2 of them are consecutive
Prove that for a square n ×n matrix A, Ax = b (1) has one and...
Prove that for a square n ×n matrix A, Ax = b (1) has one and only one solution if and only if A is invertible; i.e., that there exists a matrix n ×n matrix B such that AB = I = B A. NOTE 01: The statement or theorem is of the form P iff Q, where P is the statement “Equation (1) has a unique solution” and Q is the statement “The matrix A is invertible”. This means...
2. Suppose in a city of 10 million people, fifty percent have been infected with the...
2. Suppose in a city of 10 million people, fifty percent have been infected with the new corona virus. (i) If a sample of 204 people is selected without replacement, what is the probability that at least 105 will be infected? Give an exact expression for your answer. Do not simplify. (ii) Repeat Part (i) except assume that the sampling is with replacement. Do not simplify. (iii) Suppose that you test the 204 people one-by-one with replacement. Consider the event...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT