1975 AHSME Problem 8

If the statement "All shirts in this store are on sale." is false, then which of the following statements must be true?

I. All shirts in this store are at non-sale prices.

II. There is some shirt in this store not on sale.

III. No shirt in this store is on sale.

IV. Not all shirts in this store are on sale.

\textbf{(A)}\ \text{II only} \qquad \textbf{(B)}\ \text{IV only} \qquad \textbf{(C)}\ \text{I and III only} \qquad \textbf{(D)}\ \text{II and IV only} \qquad \textbf{(E)}\ \text{I, II and IV only}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.