An adequate set of connectives for propositional logic is a set such that for every formula of propositional logic there is an equivalent formula with only connectives from that set. for example, the set {¬,∨} is adequate for propositional logic, because any occurrence of ∧ and → can be removed by using the equivalences φ → ψ ≡ ¬φ ∨ ψ and φ ∧ ψ ≡ ¬(¬φ ∨ ¬ψ). show that eachof the following set isanadequate setof connectives for propositional logic. (in the latter case, we are treating ⊥as a nullary connective.) (hint: show that other connectives can be expressed by the given connectives.)