"The dog should be carried in the cabin and restrained" is correct. The fact that it doesn't mention the mat is misleading, but it doesn't state that there is no mat. It leaves the mat question open. There are a lot of other requirements for the flight that are not mentioned as well. The question does not specifically state that the aircraft has a current MR or is below its MTOW or that the pilot has a medical.
It is an exercise in semantics, it is misleading and as someone who obviously knows the reg it must be very frustrating for you. There are many other equally badly worded questions in the air law exam. I guess the examiners are trying not to quote whole slabs of the regs in the answers to make it very clear, as that would jog your memory and make it easy. It is one of the failings of multiple choice questions when testing something that is more complex than a simple black and white answer.
If I ask the question "Is it permissible to carry a dog in the cabin of an aircraft?", the answer is "Yes". There are other requirements, but the answer is still "Yes". The fact that compliance with the other requirements is not specified in the question does not change the answer. If I add the word 'restrained' in front of 'dog', the answer is the same. If I add 'on an absorbent mat' after 'dog' its still the same.
The exam question is misleading because it does mention one other requirement (restraint), but does not address the mat issue.
It is not 'fair', but as others have said it is time to get over it and move on.
Good luck next time around.
