Answered: Q1 Determine which of the following pairs of propositional forms are equivalent. Justify your answer without using truth tables. a) ¬p⟶(q⟶r) and q⟶(p∨r). b)… | bartleby

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∨ψand ϕ∧ψ≡(ϕ∨ψ). (a) Show that {, ∧},{, →} and {→, ⊥} are adequate sets of connectives for propositional logic. (In the latter case, we are treating ⊥as a nullary connective.)

SOLVED:Suppose P and Q are (possibly molecular) propositional statements. Prove that P and Q are logically equivalent if any only if P ↔Q is a tautology.