I am studying Lattices using the algebraic definition i.e. A set with 2 binary operations $\wedge , \vee$ that satisfies: Commutative of $\wedge$ and $\vee$
Associativity of $\wedge $ and $\vee$
Idempotency for $\wedge$ and $\vee$
Absorption law for $\wedge $ and $\vee$
And I got a question:
Every proposition true will remains true even if we change $\wedge$ and $\vee$?
For example a Lattice is distributive if $a\wedge (b\vee c) = (a\wedge b) \vee (a \wedge c)$
Or equivalently
$a\vee (b\wedge c) = (a\vee b) \wedge (a \vee c)$