# Discrete Mathematics [closed]

1. Prove that if we take 6 numbers from 1,2,3,... 10, amongst the numbers selected are two whose difference is 5.

2. Prove the set $3Z^+ =\{3,6,9,12,15\}$ is countable.

3. Decision tree is given as follows. Start with root. If yes, it goes to left, otherwise to right. Now, if a student gets average score at 83. What is his grade he will get?

-

## closed as off-topic by Cameron Buie, Rahul, The Chaz 2.0, amWhy, T. BongersFeb 27 at 21:31

This question appears to be off-topic. The users who voted to close gave these specific reasons:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, T. Bongers
• "Homework questions must seek to understand the concepts being taught, not just demand a solution. For help writing a good homework question, see: How to ask a homework question?." – Cameron Buie, Rahul
If this question can be reworded to fit the rules in the help center, please edit the question.

Welcome to Math.SE! We would love to hear your thoughts on these problems, and see your attempt as to how to solve them. :) –  anorton Jul 31 '13 at 1:31

It is little known fact that numbers have a romantic life. It turns out that $1$ and $6$ are "partners," as are $2$ and $7$, also $3$ and $8$, and $4$ and $9$, and $5$ and $10$. So we have a total of five couples. Thus if we pick six people (numbers), then they cannot all belong to different couples: at least two of the six are partners.