"Implies" is the connective in propositional calculus which has the meaning "if 
is true, then
is also true." In formal terminology, the
term conditional is often used to refer to this connective
(Mendelson 1997, p. 13). The symbol used to denote "implies" is 
, 
(Carnap 1958, p. 8;
Mendelson 1997, p. 13), or 
.
The Wolfram Language command Implies[p,
q] can be used to represent the logical implication 
.
In classical logic, 
is an abbreviation for 
, where
denotes NOT and 
denoted OR (though this is not the
case, for example, in intuitionistic logic).
is a binary operator that is implemented in
the Wolfram Language as Implies[A,
B], and can not be extended to more than two arguments.
has the following truth
table (Carnap 1958, p. 10; Mendelson 1997, p. 13).
 |  |  |
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
If 
and 
(i.e., 
), then 
and 
are said to be
equivalent, a relationship which is written symbolically
as 
, 
, or
(Carnap 1958, p. 8).
