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If the proposition $\neg P \to Q$ is true, then the truth value of the proposition $\neg P \vee ( P \to Q)$ is

1. True
2. Multi-valued
3. False
4. Can not be determined

difference between multivalued and can not be determined.  ??
A proposition cannot have multiple values at the same time as then it will violate law of non contradiction.

Here, 2nd proposition can be true or false at a time , hence based on truth values of 1st proposition , it cannot be determined or unknown .

We are getting it as Contingency ie it can be either True or False at the same time but not both ie it can not be multivalued.

Hence option D will be the right answer.
we are getting both true and false..then what will be the answer?
by
A TRUTH value of a proposition is always a single value.

It cannot be multivalued i.e. it cannot have multiple values, it can be either true or false but not both but here we are getting that sometimes it can give false and sometimes true.

Therefore it's TRUTH value cannot be determined.

Option D (Satisfiable/Contigency)

Option B is incorrect as Multi-valued propositions have multiple values simultaneously. (They're not in the GATE syllabus, I think.)

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