Prove that in two commodities world, both commodites cannot be inferior at the same time.?

Question

Prove that in two commodities world, both commodities cannot be inferior at the same time.

If you cannot solve the question, just give me the hints to catch the trick to solve the question. If you can do it Mathematically, it will be more than helpful but any other way is acceptable and is better than nothing.

Thanks

Answer 1

As long as you compare one to the other, one will be superior to the other.

Answer 2

An inferior good is a good whose demand falls when income rises. Now, suppose that there are only two goods in the world, and income rises. If the prices for both goods are unchanged, then consumption of one or both goods must rise. Demand for both goods cannnot both fall, or income would go unspent! Therefore, only one good or neither of the goods can be inferior.