One step in the synthesis of pioglitazone (trade name Actos), a drug used to treat type 2 diabetes, involves the reaction of A with B in the presence of NaH to afford C. What is the structure of C?

Pioglitazone is an oral anti-diabetic drug with a chemical formula $C_{19}{H}_{20}{N}_2{O}_{3}S$. It belongs to the thiazolidinedione class of drugs.

Other uses of the drug include the increase of HDL cholesterol, reduction of triglycerides, and reduction of plasma fatty acid levels.

It is sold under the brand name Actos and is administered along with metformin, sulfonylurea, or insulin.

Williamson ether synthesis is a method of preparation of ethers in the presence of strong bases generally sodium hydride.

In this reaction, sodium hydride abstracts a proton from the hydroxyl group to form an alkoxide ion.

Alkoxide ions are strong bases and can react with alkyl or aryl halides removing the halide group to form ethers.

The reaction is an example of Williamson ether synthesis in which the sodium hydride abstracts proton from the hydroxyl group of compound A and the ion formed reacts with compound B forming an ether linkage.