And elimination and introduction. 1. (p ^ q). (r^ s)+ (q ^ s). Implication introduction and elimination 2. (pq). (gr) + (pr). 3. Show that (p(ar)) ((p ^ q) r). Or introduction and elimination 4. (pv q)+((pq) v (qp)). 5. (p q)+((rv p) (r v q)). Miscellaneous Proofs 6. (d) p (p-q).p+q 7.rp (r-g)+p-(g ^r) 8. 8, pq-(p^q) 9. p(qr). p-q-pr 10. p q +((p ^ q) p)^(p (p ^ q)) For the sequents below, show which ones are valid and which ones are not. 1. p 2.p (p)+(-p). q. s tp vs-qat