Who is wearing a hat ?

Who is wearing a hat ?

Alex, Bob and Carl go for a walk every day.
If Alex doesn't wear a hat, then Bob wears a hat.
If Bob doesn't wear a hat, then Carl wears a hat.
Today Bob is not wearing a hat.
Who is wearing a hat?

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Answer:
Both Alex and Carl are wearing hats.

Reason:
Since Bob is not wearing a hat, Carl is wearing a hat.
Now if Alex doesnot wear a hat, than Bob must wear a hat.
But he is not wearing a hat. So it implies Alex is also wearing a hat.
So Alex and Carl are wearing hats.