a) Show that the following logical equivalences hold for the Peirce arrow↓, where P ↓Q = ~ (P ∨ Q). P ∨ Q = (P ↓ Q) ↓ (P ↓ Q) P ∧ Q= (P ↓ P) ↓ (Q ↓ Q) b) Show that for the Shuffer stroke | P ∧ Q = (P | Q) | (P | Q) c) Use the result from (b) and example 2.4.7 from book to write P ∧ (∼Q ∨ R) using only Shuffer strokes
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(a) By the definition of piece arrow-
We have derived that is logically equivalent with ~P
(b) =(~( (~
(c) =(~( (~(