Logic is very sharp and most of the times need not necessarily lead us to the truth. Logic is indication of possessing incisive intellect.
See the following example:
Gauss is a great mathematician. Once his teacher asked a question in their class.
The question is "How many stars are there in the Universe?". And also added, if the answer is correct, he will ask the next question.
Gauss told some number.
The teacher asked, "how do you know?"
Gauss then said this is the second question sir!
Logically the answer is true because the teacher said if the answer is correct he will ask the nest question. And he asked the next question, "how do you know?".
Whatever might be the meaning of that question, because that is the second question, the answer given by Gauss is to be correct logically.
And most of the times logic takes us somewhere and not necessarily leads towards the Truth. We must not depend on mere logic to know the Truth. We must be able to discriminate. Then at least we know what is not Truth.