Cigol is a student who dislikes truth tables. Cigol is considering statements that are made out of statements P and Q (possibly repeated), together with the symbols ∨, ∧, and ∼. Cigol will call two statements “related” if they agree in at least three of the four columns of a truth table. For example: the statements P ∨Q and (P ∨Q)∧ ∼ (P ∧Q) agree in three cases (P and Q both false; P true and Q false; P false and Q true), so Cigol calls them related.
Show that Cigol’s relation is not an equivalence relation.