Let $c_{uo}$(K, L) denote the price of a 1-year Apple European down-and-out call with strike $K$ and barrier $L$.
Assume the spot price is $80$. Using only no-arbitrage, describe as many (in)equalities that can be derived comparing the five quantities: $$0, c_{uo}(101, 120), c_{uo}(101, 110), c_{uo}(111, 110)$$
From what I can understand, when we have a fixed K with no arbitrage, the price of the lower barrier is more than (or equal to) the price of the higher barrier.
How does the spot price and K enter these comparison?