In the short run,
unemployment and inflation are positively related. in the long run they are largely unrelated problems.
and in the long run inflation and unemployment are positively related.
unemployment and inflation are negatively related. in the long run they are largely unrelated problems.
and in the long run inflation and unemployment are negatively related.

The correct answer is: unemployment and inflation are negatively related. In the long run they are largely unrelated problems.

Explanation:

According to the Philips curve, in the short run, inflation and unemployment rate are inversely related. This implies that when inflation decreases, the unemployment rate increases.  

This is indicated by the downward-sloping Phillips curve. When the government adopts a contractionary policy to reduce inflation, unemployment will increase.  

In the long run, the Phillips Curve will be a vertical line at the natural rate of unemployment. The inflation rate is not related to the unemployment rate in the long run.

metallurgy is your answer

the "study of metals and the process of refining ("

note that it says metal. metallurgy has the word "metal" in it, and so is most likely your answer (and is your answer).

~