Propositional Logic

Propositional and First Order Logic.

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.)

Truth Tables and Logical Statements | IIT JEE Study Material

suppose that a truth table in n propositional variables is specified show that a compound proposition with this truth table can be formed by taking the disjunction of conjunctions of the var 32642