An old man with a cowboy hat, cowboy boots, and blue jeans stands next to a cabin and looks off into the distance as the sun sets in the background.
Nobody has a hat
If somebody is there with a hat, then it's not true that nobody has a hat.
Nobody cannot have a hat if an old man is wearing a cowboy hat.
An old man with a cowboy hat, means it is wrong to say that nobody has a hat.