Question: 1) How can I do this only using methods from mathematical logic and in particular Posts Theorem is not allowed to be used. Show that

1) How can I do this only using methods from mathematical logic and in particular Posts Theorem is not allowed to be used.

Show that (solve with no truth tables only through mathematical logic (logical axioms))

(p(pq))p

2)How can I do this only using methods from mathematical logic and in particular Posts Theorem is not allowed to be used.

Show that (solve with no truth tables only through mathematical logic (logical axioms))

(q(q))(p(p))

3) Show that (deduction theorem can be used also no truth tables allowed to solve only mathematical logic) In particular Posts Theorem is not allowed to be used.

(pq)(q(rp))

4) How can I do this only using methods from mathematical logic and in particular Posts Theorem is not allowed to be used.

Show that

(p(qp))(qp)

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