Let (nand) and (nor) be binary connectives defined by the following truth table:
| p | q | (nand) | (nor) |
|---|---|--------|-------|
| T | T | F | F |
| T | F | T | F |
| F | T | T | F |
| F | F | T | T |
3. (3 points) Show the following sets of connectives are adequate:
a) {ΓΒ¬, Γ’ΛΒ§} (6) {ΓΒ¬, Γ’ΛΒ¨}
Hint: Recall {ΓΒ¬, Γ’ΛΒ§} and {ΓΒ¬, Γ’ΛΒ¨} are both adequate.
(a) (5 points) Find a formula w Γ’ΛΛ Form(L[S]) logically equivalent to (p1 Γ’ΛΒ§ p2), where S = {ΓΒ¬, Γ’ΛΒ§} and S = {ΓΒ¬, Γ’ΛΒ¨}.
(b) (1 point) Briefly explain why it is not always preferable to formulate propositional logic in a language with as few connectives as possible.