When talking about the supply curve, does a price increase always result in an increase in quantity sold?

I thought I had an understanding of the law of supply (i.e that when price increases supply should also increase) but we were asked a question on a recent homework sheet that kind of puzzled me. the question is as follows "true or false, Since supply curves slope upwards, we would never see an outcome in a market where the price increases and the quantity sold decreases.?". My initial thoughts were no as the laws of supply dictate a sales increase but the question made me second guess so I thought I would ask if indeed there are any exceptions which make this question false because the prof said something like this could come up on the final.

1. Law of supply states that quantity supplied increases in price.

2. Quantity supplied $$\neq$$ quantity sold.

For example if we have supply given by:

$$S= 10 +p$$,

then if price 1 quantity supplied is 11, when price is 10 quantity supplied is 20 and so on. So clearly, quantity supplied increases in price.

However, quantity sold does not depend just on supply but also demand. For example, if demand is given by:

$$D=100-p$$

at price 1 quantity demanded is 99 units, but at price 1 firms are only willing to supply 11 units, so demand cannot be satisfied and there is a shortage of 88 units, since only 11 units can be sold.

However, at price 60, quantity demanded is 40, but quantity supplied is 70, so we have surplus. Quantity sold is 40, because even though firms are willing to supply 70 units only 40 can be sold. Quantity sold is always given by an interior point along demand supply, so above equilibrium price quantity sold is determined by what consumers demand, and below equilibrium price by what firms are willing to supply.

It is possible to see an outcome where equilibrium quantity sold decreases and the price increases when the supply curve is upward sloping. Consider an increase in price of input labor from $$w_0$$ to $$w_1$$. This increase in input prices will lead to a leftward shift of the supply curve. The reason is that the producer would like to supply a smaller quantity at any given price because of the higher cost of production. This would lead to increase in equilibrium price and fall in equilibrium quantity sold, given that the demand curve is downward sloping. Here is the picture:

As we can observe, as a result of an increase in the wage rate from $$w_0$$ to $$w_1$$, the equilibrium price has gone up from $$p_0$$ to $$p_1$$, but the equilibrium quantity has come down from $$q_0$$ to $$q_1$$.

This is a trick question, apparently with an educational intent.

Supply and Demand curves are curves that reflect intentions, not realized events.

Statement A: Supply curves slope upwards

is translated "at higher prices suppliers are willing to sell more ("willing" = intention)

while

Statement B: The price increases and the quantity sold decreases

is a realized event.

This event is certainly influenced by the previously stated intention, but it is not fully determined by it, so they can certainly co-exist, as the other answers exemplified.