. Let Ipl be the smallest set of propositional logic formulas such that: Base case: Variables P, Q, R, ... are in Ipl. Constructor case: If e, f e Ipl, then (e IMPLIES S) E Ipl. Here are some examples of formulas that are in Ipl: P, (R IMPLIES S), ((P IMPLIES P) IMPLIES (R IMPLIES R)). Use structural induction to prove that no formula in Ipl is logically equiv- alent to NOT(P). . Let Ipl be the smallest set of propositional logic formulas such that: Base case: Variables P, Q, R, ... are in Ipl. Constructor case: If e, f e Ipl, then (e IMPLIES S) E Ipl. Here are some examples of formulas that are in Ipl: P, (R IMPLIES S), ((P IMPLIES P) IMPLIES (R IMPLIES R)). Use structural induction to prove that no formula in Ipl is logically equiv- alent to NOT(P)