Question #178255

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

Expert's answer

(a) By the definition of piece arrow-

~

=~

We have derived that is logically equivalent with ~P

~

(b) =(~( (~

(c) =(~( (~(

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