Hey,

can you help me in this proofs?

This pic shows example.

This is the other proofs.

Thanks

is to exhibit a proof of using given axioms, given or previously established inference rules, and , ,an as a sumption. For exarnpk, to say a logician urute s to be given the followizg belief derne (we call an inference rule relating to what the lagician beleves a "behef scheme TP We prove that the following is a valii bebef scheme for an accurate logician Bp by way of proof by contradiction, which alows one to use the negation of what is to be proved as an axiom 1. Bp 2. p 3. -Bp given asumption (begin proof by contradiction) the logician is accurate 5. (Ep -BP) p tautology ((as a6JA a.) a6 is a tautology (end proof by contradiction) Item 2 (above) assumes the negation of what is to be proved; in particular, it must be the negation of the last element of the list constituting the proof. Item 3 results from applying the belief scheme for an accurate logdan to item 2. Item 4 results fra applying the following inference rule to items 1 and Item 6 results from applying the fllowing inference ule to items 4 and 3