$\def\op{\mathbin{\#}}\def\R{\mathbin R}$Original question:
A logical operation between two propositions $p$ and $q$ is denoted as $p\op q$. It is only true when $p$ is true and $q$ is false; otherwise it is false. Let $R$ be a relation on the set of ordered pairs of propositions, where $R$ is defined as follows:
$\bigl((a,b),(c,d)\bigr) ∈ R$, if and only if $(a \land b) \op (c \vee d)$ is true.
Is R an equivalence relation?
For symmetric, the rule is $∀a,b ∈ B$ s.t. $a\R b$, $b\R a$ is true.
But when I do the relation, do I bring the operator (i.e. $\land$ and $\lor$) over also?
For example:
1) $(a \land b) \op (c \lor d) \to (c \lor d) \op (a \land b)$
2) $(a \land b) \op (c \lor d) → (c \land d) \op (a \lor b)$
which is the correct way of representing?