Prove that, for any integer n ≥ 1, there is an n-variable logical proposition ϕ in conjunctive normal form such that the truth-table translation to DNF (from Theorem 4.11) yields an DNF proposition...

Prove that, for any integer n ≥ 1, there is an n-variable logical proposition ϕ in conjunctive normal form such that the truth-table translation to DNF (from Theorem 4.11) yields an DNF proposition with exponentially more clauses than ϕ has.