Provide proofs for the following arguments. You may use both primitive and derived rules of inference. 18. (∀y)Py (∃x)Px

[answerhappygod]

Provide proofs for the following arguments. You may use bothprimitive and derived rules of inference.
18. (∀y)Py
(∃x)Px ≡ Rx
∴ Rx
19. (∃z)(∃y)(Tz ⊃ By)
∴ (∀z)Tz ⊃ (∃z)Bz
20. (∀x)~Rx
(∃z)[Pz ⊃ (∀y)(Py ⊃ Ry)]
∴~(∀x)Px
21. b = c
∴ Bc ≡ Bb
22. ∴ (∀x)(Px v ~Px) ((Provide a proof with no premises; thissentence is a logical truth. Hint: you can use assumptions.)