Is $ R = \{ (A,B) \in \Omega² \quad| \quad A \land B \} \quad$ with $\Omega = \{ A\quad| $ A is a proposition $ \}$ reflexive?

Question

Is $ R = \{ (A,B) \in \Omega² \quad| \quad A \land B \} \quad$ with $\Omega = \{ A\quad| $ A is a proposition $ \}$ reflexive?

I assume that you have to consider untrue propositions, too.

$A \land A = 1$ for $A = 1$, but $ A\land A = 0 $ for $A=0$

Since $ R $ is symmetric and transitive, I'm confused about its reflexivity.

$A \land B = 1$ for $A = B = 1$, but $ A\land B = 0 $ for $A=0$ or $B=0$

Answer 1

Your doubts are justified.

For $R$ to be reflexive, you must have $(A,A)\in R$ for all propositions $A\in\Omega$.

But you don't. Whenever $A$ is false, you have $A\land A = 0$. Therefore $A\not\in R$.