Conjunction: In logic: Logical term for and.
Four basic rules for the logical term 'and' (see: Natural Logic) that relate to how the term 'true' applies or fails to apply to statements with 'and' are:
and1: If .X and Y. is true, then .X. is true.
and2: If .X and Y. is true, then .Y. is true.
and3: If .X and Y. is not true, then .X. is not true or .Y. is not true.
and4: If .X. is not true or .Y. is not true, then .X and Y. is not true.
The last two of these rules lead to what are known as De Morgan's laws, that relate 'and', 'or' and 'not' to the following effect:
.X and Y. is true IFF .not (not X or not Y). is true
.X or Y. is true IFF .not (not X and not Y). is true
The truthtable for 'and' also written as '&' is
P 
Q 
P&Q 
T 
T 
T 
T 
F 
F 
F 
T 
F 
F 
T 
F 
which also conforms to the above rules, supposing that every statement is true (T) or not (F).
It should be noted that conjunction is more complicated when probabilities are involved, since then the analysis and definition of conjunction comes to this, with the help of the notion of conditional probability:
p(X and Y) = p(YX)*p(X)
This analysis becomes possible because probabilities are numbers between 0 and 1 inclusive.
