Hi Jet. Yes, the reward for the 2nd Furniture Set is a black and white checkerboard rug. Unless something has changed, a tent is not required to complete the set. If you're referring to the last item, it's a hammock, which is available in the "Outdoors" section of the Store. The hammock also has a banner that says "Furniture Set" on its Store listing (all items required to complete the furniture sets do). If your game shows something different do let us know.