What have you tried? What's the definition of a relation? Reflexive relation? Symmetric relation? Transitive relation?
Showe some work.
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 ???
The answer to A) depends on your textbook. It may be 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 .
But there are reflexive relations.
And there are symmetric relations.