Each of a b c was in the shop on the day of the robbery and


There are 3 suspects, A, B, and C, for a robbery that presumably happened in a shop. We know that the following facts are true:

(1) Each of A, B, C was in the shop on the day of the robbery, and no one else was there on that day.

(2) If A was guilty, then he had exactly one accomplice.

(3) If B is innocent, then so is C.

(4) If exactly two are guilty, then A is one of them.

(5) If C is innocent, then so is B.

Was there a robbery in the first place?

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Algebra: Each of a b c was in the shop on the day of the robbery and
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