logic - What does the semantic entailment relation mean (M |= A)? -

i read many acticles it. described :

in logics, meaning described satisfaction relation

m |= a

that describes when situation m satisfies formula a.

so, searched examples. found examples following :

true |= false = false

false |= true = true

i don't understand @ all. mean in these cases?

(assuming talk propositional logic (it similar other logics such pred. logic))

for 2 formulas , b:

a |= b  "b evaluates true under evaluations evaluate true" 

for set of formulas m , formula b:

m |= b "for every evaluation: b evaluates true if elements of m  evaluate true" 

coming examples:

true |= false  incorrect since evaluations exist   false |= correct formula a, since 'false' never evaluated 'true' under evaluation 

rgrds.