| (TTTT)(p, q)
|
Tautology
|
(if p then p, and if q then q.) [p ⊃ p . q ⊃ q]
|
| (FTTT)(p, q)
|
in words:
|
Not both p and q. [~(p . q)]
|
| (TFTT)(p, q)
|
” ”
|
If q then p. [q ⊃ p]
|
| (TTFT)(p, q)
|
” ”
|
If p then q. [p ⊃ q]
|
| (TTTF)(p, q)
|
” ”
|
p or q. [p ∨ q]
|
| (FFTT)(p, q)
|
” ”
|
Not q. ~q
|
| (FTFT)(p, q)
|
” ”
|
Not p. ~p
|
| (FTTF)(p, q)
|
” ”
|
p or q, but not both. [p . ~q : ∨ : q . ~p]
|
| (TFFT)(p, q)
|
” ”
|
If p, then q; and if q, then p. [p ≡ q]
|
| (TFTF)(p, q)
|
” ”
|
p
|
| (TTFF)(p, q)
|
” ”
|
q
|
| (FFFT)(p, q)
|
” ”
|
Neither p nor q. [~p . ~q or p | q]
|
| (FFTF)(p, q)
|
” ”
|
p and not q. [p . ~q]
|
| (FTFF)(p, q)
|
” ”
|
q and not p. [q . ~p]
|
| (TFFF)(p, q)
|
” ”
|
q and p. [q . p]
|
| (FFFF)(p, q)
|
Contradiction
|
(p and not p; and q and not q.) [p . ~p . q . ~q]
|