5.101 The truth-functions of a given number of elementary propositions can
always be set out in a schema of the following kind: (TTTT) (p, q)
Tautology (If p then p, and if q then q.) (p z p . q z q) (FTTT) (p, q) In
words : Not both p and q. (P(p . q)) (TFTT) (p, q) " : If q then p. (q z p)
(TTFT) (p, q) " : If p then q. (p z q) (TTTF) (p, q) " : p or q. (p C q)
(FFTT) (p, q) " : Not g. (Pq) (FTFT) (p, q) " : Not p. (Pp) (FTTF) (p, q) "
: p or q, but not both. (p . Pq : C : q . Pp) (TFFT) (p, q) " : If p then
p, and if q then p. (p + q) (TFTF) (p, q) " : p (TTFF) (p, q) " : q (FFFT)
(p, q) " : Neither p nor q. (Pp . Pq or p | q) (FFTF) (p, q) " : p and not
q. (p . Pq) (FTFF) (p, q) " : q and not p. (q . Pp) (TFFF) (p,q) " : q and
p. (q . p) (FFFF) (p, q) Contradiction (p and not p, and q and not q.) (p .
Pp . q . Pq) I will give the name truth-grounds of a proposition to those
truth-possibilities of its truth-arguments that make it true.


5.11 If all the truth-grounds that are common to a number of propositions
are at the same time truth-grounds of a certain proposition, then we say
that the truth of that proposition follows from the truth of the others.


5.12 In particular, the truth of a proposition 'p' follows from the truth
of another proposition 'q' is all the truth-grounds of the latter are truth-
grounds of the former.


5.121 The truth-grounds of the one are contained in those of the other: p
follows from q.