Binary Relations

[devil2euz]

I'm struggling to understand binary relations in discrete mathematics.Can anyone solve these for me?

1.
Let A be {5,10,15,20,25,30,35,40,45,50,55}
aRb if a's and b's smallest prime divisors are the same.
Define the equivalence classes.

2.
Let A be {2,6,10,18,25,50,60,75,150}
a≼b if a|b
Define the set of the maximum elements of the ≼ by listing them.

Sorry for the grammatical mistakes.

 

[Dr.Peterson]

I'd start problem 1 by listing the smallest prime divisor of each element of A:

5: 5​

10: 2​

15: 3​

and so on. Then all numbers with smallest prime divisor 2 are related, for instance. Can you take it from there?

For problem 2, I can think of several ways to start, but one would be to make a table listing elements of A across the top and down the left side, and indicate which pairs are related by "≼", that is, "row ≼ column". Then use that to identify which numbers are maximal.

If you need more help, you might tell us the definitions you have for equivalence class and for maximum element, so we can discuss how they apply.

 

[pka]

Let A be {5,10,15,20,25,30,35,40,45,50,55}
aRb if a's and b's smallest prime divisors are the same.
Define the equivalence classes.

Lets deal with this one first.
Is it clear to you that \(5\mathcal{R}55~?\) But why is it true that \(5\cancel{\mathcal{R}}10~?\)
Can you list all the terms \(\{x\in A: (5,x)\in \mathcal{R}\}~?\)
After you answer we can proceed. If you have more questions state them.

 

[devil2euz]

Thank you so much for your help! I could finish my test 100/100pts with your advices.
Sorry if it was hard to figure out what were the tasks about,I tried to translate them from my language to english as accurate as I could.

 

[Dr.Peterson]

Thank you so much for your help! I could finish my test 100/100pts with your advices.
Sorry if it was hard to figure out what were the tasks about,I tried to translate them from my language to english as accurate as I could.

I had no trouble at all understanding the question; your English is far better than my _____ (fill in the blank)! I wouldn't have known it was not your language, or that you had translated.

And clearly you understand the mathematics, since although you asked us to solve the problems for you (which is not what we do), a starting hint was all you needed. Good work.