Answer to Question #178255 in Discrete Mathematics for Ayesha

Question

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

Answer 1

(a) By the definition of piece arrow-

   

   ~

 

   =~

  We have derived that is logically equivalent with ~P

      ~

(b) =(~( (~

                      

(c) =(~( (~(