Recent content by Lancelot1

Dear All, I am trying to solve the attached two questions. In both I need to determine if the relation is an equivalence relation, to prove it if so, and to find the equivalence classes. In both cases it is an equivalence relation, and I managed to prove both relations are reflexive. Now I...

Hi all, I need some help with this one:There are 3 shapes of pasta: 1,2,3. In a box there are 3 packages of pasta of shape 1, with different weights: 300 gr, 400 gr, 500gr. In addition, there are 5 packages of paste of shape 2, with weights: 300gr, 350gr, 400gr, 500gr, 600gr, and 4 packages...

Hello, Another combinatorical question I scratch my head with. In a parliament of a country there are 400 seats that should be divided between 3 parties. What is the number of possibilities of division if we want that no party will have more than 200 seats ? Each party must have at least one...

Dear all, I am trying to calculate this one, I can't think of a way to calculate it.. A standard deck of cards is given with 13 cards of 4 shapes ( Clubs , Diamonds , Hearts , Spades ). What is the number of possibilities to order the cards in the deck such that a king won't be on top of an...

Two numbers are bring chosen by random from the set {1,2,3,4,5}. If the sum of the two numbers is even, you win 100 dollars, otherwise you win nothing. In order to participate in the game, you pay $80. What is the expected value and variance of the profit after 17 games ? I solved this one...

Thank you !

Do you mean that the answer is : \[\binom{11}{3}\] ? I don't understand the rational behind it.

Hello all Please look at this questions: What is the number of permutations for creating a code of 3 digits from the digits 1,2,3,...,9 , such that every digit is equal or larger from the previous one ? I know that if I wanted the number of permutations without restrictions it would be...

Hello all, I am trying to solve this one: John has n friends . He wants to invite in each evening (365 days a year) three of his friends for dinner. What should be the size of n, such that it will be possible not to invite the same triplet twice ? What I did was: \[\binom{n}{3}\leq 365\]...

Dear All, I am trying to prove the following identity: \[\binom{n}{k}=\binom{n-2}{k}+2\binom{n-2}{k-1}+\binom{n-2}{k-2}\] My attempt was based on transforming the binomial coefficients into fractions with factorials, and then elimintating similar expressions. Somehow it didn't work out. I...

Hi guys I can't figure this one out. I tried to use truth tables, but never found an equivalence , no matter which of the 5 options I tried. It is given that $\alpha$ is logically equivalent to $\alpha \rightarrow \sim \beta $ . Which of the following is a tautology ? 1) $\alpha$ 2) $\beta$...

Hello all, Is this statement true ? Is every increasing monotonic function in a closed interval also continuous ? How do you prove such a thing ? Thank you !

Dear all, I am trying to figure out if a non continuous function is also not bounded. I know that a continuous function in an interval, closed interval, is also bounded. Is a non continuous function in a closed interval not bounded ? I think not, it makes no sense. How do you prove it ? Thank...

When I try to look at the derivate by y, I go up and down the y-axis, the level curves are constant there, am I wrong ?

Hello all, I have encountered a very difficult question in geometry. The question has several parts. I really need your help. I have tried solving the first and second ones, not sure I did it correctly, and certainly don't know how to proceed and what the results means. I would really...