Anindya - very nice! Maybe someone else can make a slick electronic version suitable for a coffee table book. But your picture shows how to walk from 11 to 13 by an alternating sequence of \\(\sim_P\\) and \\(\sim_Q\\) steps, proving that

$$ 11 \sim_{P \vee Q} 13 $$

even though

$$ 11 \nsim_P 13 $$

and

$$ 11 \nsim_Q 13 $$