"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 
 denotes 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).
 
         
	    
	
    
