Multivalued vs can not be determined If the proposition $¬p→q$ is true, then the truth value of the proposition $¬p∨(p→q)$, where $¬$ is negation, $∨$ is inclusive OR and $→$ is implication, is


*

*True

*Multiple Values

*False

*Can not determined 



My attempt :
One of the my friends it explained as :
From the axiom $¬p→q$, we can conclude that $p+q$.
So, $p$ and $q$ can be True or False, i.e. nothing can be said about it's value.
$≡¬p∨(p→q)$
$≡¬p∨(¬p∨q)$
$≡¬p∨q$
Since nothing can be said about the Truth value of $p$ and $q$, it implies that $¬p∨q$ can also be True or False.
Hence, the value cannot be determined.
My question is : 

Why not multiple Values? What is difference between them, please, explain it with suitable example. 


Your reasoning is invalid. "$p \lor q$" does not imply that $p,q$ can be anything, but rather that at least one of $p,q$ is true. Checking all 3 cases shows that "$\neg p \lor q$" would be true in 2 cases and false in 1 case. Therefore it has multiple possible truth values. I presume that "cannot be determined" is for when you cannot even tell whether it has a single or multiple possible truth values. However, I agree with Mauro that ultimately the justification for classical logic is the assumption that every precise declarative sentence is either true or false and not both, in its context, and so the question is a terrible one.
