Yes - I was given a syllogism that was logically correct but the Truthyness of the premises where wrong or misleading in the real world.

All pilots need a medical exam to have a license.

John is a pilot.

John has had a medical exam.

Pilots can be licensed without a medical exam. It is illegal for them to fly without a valid medical but the 2 are separate issues. Also LSA pilots do not need a medical.