How many Boolean algebras are there with four elements $0,1,a,b$ ?

I don't know how to proceed with this.

Any ideas ?



Try to fill out the multiplication and addition tables.

For addition, $a+1$ can't be zero because 1 is its own additive inverse. $a+1$ can't be 1 because that would imply $a=0$. The sum can't be $a$ because that would imply $0=1$. So there is only the possibility that $a+1=b$.

From this you an deduce what $a+b, b+1$ and $ab$ have to be.

Once you have this, compare it to $F_2\times F_2$ where $F_2$ is the field of two elements.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.