(a) Yes (b) No?
(b) No in most cases.
This is one of those questions I dread getting at a dinner party or from a fellow parent while standing at the sidelines watching our kids play sports. It speaks to most people who do not see the connection between taxation and expenses and the ultimate political motivations for making some things deductible and others not deductible.
Going back to the question. The longer answer is that the dog must be connected to revenue and the expense of the dog’s care and the cost of the dog must be reasonably connected to an expectation of profit. Going one conceptual level up; income taxation is tied to revenue sources but expenses are allowed to be recognized against those revenue sources so that tax is only charged on net profits.
If the dog is a pet, then it is not deductible.
If the dog is a working dog; for example, the dog pulls a dog sled carrying tourists that pay for that experience or the dog is “employed” by a security company to patrol a building that the security company is paid to protect, then the dog is deductible.