r 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.

5.122 If p follows from q, the sense of 'p' is contained in the sense of
'q'.

5.123 If a god creates a world in which certain propositions are
true, then by that very act he also creates a world in which all the
propositions that follow from them come true. And similarly he could not
create a world in which the proposition 'p' was true without creating
all its objects.

5.124 A proposition affirms every proposition that follows from it.

5.1241 'p. q' is one of the propositions that affirm 'p' and at the
same time one of the propositions that affirm 'q'. Two propositions are
opposed to one another if there is no proposition with a sense, that
affirms them both. Every proposition that contradicts another negate it.

5.13 When the truth of one proposition follows from the truth of others,
we can see this from the structure of the proposition.

5.131 If the truth of one proposition follows from the truth of
others, this finds expression in relations in which the forms of the
propositions stand to one another: nor is it necessary for us to set up
these relations between them, by combining them with one another in a
single proposition; on the contrary, the relations are internal,
and their existence is an immediate result of the existence of the
propositions.

5.1311 When we infer q from p C q and Pp, the relation between the
propositional forms of 'p C q' and 'Pp' is masked, in this case, by our
mode of signifying. But if instead of 'p