A woman is walking her dog along a snowy ground.
A woman and her cat are laying by the fireplace.
The woman can't do two things at once, she is either walking the door or lying by the fireplace. It is also either a dog or a cat.
A dog cannot be a cat and snowy ground cannot be a fireplace.
Woman cannot be walking and laying at the same time. It is implied in the first that the woman is without her cat in the first.