# discrete math relations simple problems help !!!!

• Dec 2nd 2012, 07:30 AM
ujnikm
discrete math relations simple problems help !!!!
hello everyone

pllz give me the final result for these problems ???!!!!

Attachment 26021
• Dec 2nd 2012, 07:53 AM
Siron
Re: discrete math relations simple problems help !!!!
What have you tried? What's the definition of a relation? Reflexive relation? Symmetric relation? Transitive relation?
Showe some work.
• Dec 2nd 2012, 08:51 AM
ujnikm
Re: discrete math relations simple problems help !!!!
I know them and they are
Reflexive relation R on A, if ∀a ∈ A, (a, a) ∈ R.
Symmetric relation R on A, if ∀a∀b ∈ A, (a, b) ∈ R → (b, a) ∈ R.
Antisymmetric relation R on A, if ∀a∀b ∈ A, (a, b) ∈ R ^ (b, a) ∈ R → a=b.
Transitive relation R on A, if ∀a∀b∀c ∈ A, (a, b) ∈ R ^ (b, c) ∈ R → (a, c) ∈ R.

In the second question A) it's every thing except antisymmetric
b) is symmetric only

In the first one A) 2^16
B)2^12 , 2^10

Am I right ???
• Dec 2nd 2012, 09:25 AM
Plato
Re: discrete math relations simple problems help !!!!
Quote:

Originally Posted by ujnikm
In the first one A) 2^16
B)2^12 , 2^10
Am I right ???

The answer to A) depends on your textbook. It may be $2^{12}-1$ because some authors do not allow an empty relation.

The answer to B) depends on how you are reading the question.
I read it as, "How many relations are reflexive and symmetric.
That would be $2^6$.

But there are $2^{12}$ reflexive relations.
And there are $2^{10}$ symmetric relations.