Well if its a "real word" may depend on dialect, or where your from specifically. There are many words in Texas not really recognized as "real words" like "y'all" or many things like that. Perhaps it is a word somewhere. But I have never heard it. Remember, language is like a liquid, always shifting, and changing.
Rational and logical are quite similar in meaning but rational is something that has logic. These two words are close synonyms and not antonyms.
Answer:
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The answer would be a or b