hello everyone
pllz give me the final result for these problems ???!!!!
discrete1.bmp
hello everyone
pllz give me the final result for these problems ???!!!!
discrete1.bmp
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 $\displaystyle 2^{12}-1$ 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.