i have recently seen a question that is stated as " p does not implies q " but due to confusion i have seen a similar question on stack exchange but there is a problem on stack exchange which i do not understood, so here it is .
" p implies q " means if "p" is true then "q" must be true . taking this similar analogy for " p does not q", the statement means if P is true then "q" may or may not be true ( as implication does not hold ) and in both cases the argument will be true unlike for " p implies q" where it becomes false when "P" is true and "q" is false.
Now the answer that i have seen said that " P does not implies q " means this " - ( P -> Q ) " . but normally it means that ( p ->q ) is not always true . which to me does not make any sense because the same could be said for "P implies q " that is also not true always .
here i may have written something wrong but that is what i know . So please tell me the difference between the both , hopefully a truth table will clarify more . And if ambiguity exists somewhere here then please let me know in what circumstances the care should be taken.