The late 19th century philosopher Charles Peirce...
a) Express ¬p using only the Sheffer stroke operation ↑ (up arrow).
b) Express p v q using only the She®er stroke operation ↑ (up arrow). Justify your answer (e.g. using a truth table).
c) Explain why the set of operators ↑ (up arrow) is functionally complete .
d) Express the Sheffer stroke operation p ↑ q using only the Peirce arrow CS173 Discrete Mathematical Structures ↓ operation. Explain why the set of operators {↑} is functionally complete.
The late 19th century philosopher Charles Peirce (rhymes with `hearse,' not `fierce') wrote about a set of logically dual operators and, in his writings, coined the term `Ampheck' to describe them. The two most common Ampheck operators, the Peirce arrow (written ↓) and the Sheffer stroke (written ↑), are defned by the following truth table.
p q p ↑ q p ↓ q
T T F F
T F T F
F T T F
F F T T