And:
In
logic: Term for conjunction, both, each. The
term 'and' is a
logical term, and is used to
convey that the statement in which it occurs, provided it occurs as a
connective between statements, is such that each of the two or more statements
it is used to connect is true.
In formal logic, 'and' is often written as '&' or '.' and rules that are
adopted for '&' are often these:
From (A&B) it follows that (A).
From (A&B) it follows that (B).
From (A) and (B) it follows that (A&B).
That is: From a conjunction one can derive each conjunct, and conversely
one can derive a conjunction from having already derived each conjunct
separately.
In standard propositional logic, there is an equivalence for conjunction
that is known since antiquity, and usually goes by the name of the English
19th Century mathematician and logician De Morgan:
(A&B) IFF ~(~AV~B)
Thus one can define 'and' in terms of 'or' and 'not'.
Some other theorems in standard propositional logic involving 'and': T1.
p&p iff p
T2. p&q iff q&p
T3. p&(q&r) iff (p&q)&r
