hello everyone

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

Attachment 26021

Printable View

- Dec 2nd 2012, 06:30 AMujnikmdiscrete math relations simple problems help !!!!
hello everyone

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

Attachment 26021 - Dec 2nd 2012, 06:53 AMSironRe: 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, 07:51 AMujnikmRe: 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, 08:25 AMPlatoRe: discrete math relations simple problems help !!!!

The answer to A) depends on your textbook. It may be $\displaystyle 2^{12}-1$ 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 $\displaystyle 2^6$.

But there are $\displaystyle 2^{12}$ reflexive relations.

And there are $\displaystyle 2^{10}$ symmetric relations.