is it possible for both employment and unemployment rates to rise at the same time? explain?

Answer 1

It depends on the base you're using for both rates. If the base is the same (let's say the "active population", people working or actively looking for a job), then employment and unemployment are mutually exclusive, and both rates can't rise at the same time.
But employment rate can be calculated using the total population as base (and it is often calculated this way), and in this case employment rate (based on total population) and unemployment rate (based on active population) can rise at the same time: employment rate rising means that more people "enter the job market" (for example, if a financial crisis makes capitalisation pensions worthless, then pensioneers have to work again), and unemployment rate rising means that the economy can't create enough jobs for these people (specifically, that the proportion of people entering the market and not finding a job is higher than the previous unemployment rate).

Answer 2

Yes. Because of a growing population the economy must create about a million jobs a year just to keep the unemployment constant. If employment increases by only 100,000, the unemployment rate will increase.

Answer 3

It depends on the scale you're looking at. You could be comparing the automotive industry and the entire US. The automotive industry could be in a slump and therefore they may have to lay off workers, but the US economy could be doing fairly well and could have rising employment. So like I said, it depends....