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.