let a be the quotient algebra of formulas corresponding to propositional logic with infinitely many statement letters a is atomic b a is infinite c a has finitely many atoms d none of the th 57359

An adequate set of connectives is a set such that for every formula there is an equivalent formula with only connectives from that set. For example, the set {, V} is adequate for propositional logic, because any occurrence of ∧and →can be removed by using the equivalences ϕ→ψ ≡ϕ∨ψ ϕ∧ψ ≡(ϕ∨ψ) . (a) Show that {, ∧},{, →} and {→, ⊥} are adequate sets of connectives. (In the latter case, we are treating ⊥as a nullary connective.) (b) Show that, if C ⊆{, ∧, ∨, →, ⊥} is adequate, then ∈C or ⊥∈