logical implication
a proposition 
logically implies the proposition 
if in every model in which 
is true, is also true. we write 
. the former is called the antecedent, and the latter is called the consequent.
a set of propositions 
logically implies the proposition if in every model in which all propositions of are correct is also correct. we write 
.
there is a slight difference between logical implication and material implication, as the latter is more "primitive".
logically implies the proposition if in every model in which is true, is also true. we write . the former is called the antecedent, and the latter is called the consequent.
a set of propositions logically implies the proposition if in every model in which all propositions of are correct is also correct. we write .
there is a slight difference between logical implication and material implication, as the latter is more "primitive".
let 
| A | B |  |  |
|---|---|---|---|
| F | F | T | F |
| F | T | T | F |
| T | F | F | F |
| T | T | T | T |