You've had a bunch of problems where, given a logical formula, you can writedown the truth table. How about the reverse? That is, if I give you a truth table, canyou always come up with a formula that would give you exactly that truth table?How might you do that?
A set S of logical connectives is called universal if for any statement using allthe connectives we know (i.e. { ¬, ∨, ∧, →, ↔, }) there is a logically equivalentstatement using only the connectives in S.1. Prove or disprove: The set {¬, ∨, ∧} is universal2. Prove or disprove: The set {¬, ∨} is universal