The verb TO PURSUE, pronounced /pɚˈsuː/, has a couple of meanings:
1) to follow and try to catch or capture sb or sth for usually a long distance or time:
The dogs pursued their prey for hours.
The killer is being pursued by police in several states.
2) to try to get or do sth over a period of time:
If you decide to pursue a career in medicine, it’s not going to be quick and easy.
He got a job after he graduated, but his twin brother decided to pursue an academic degree.
3) to engage in sth:
You should pursue a hobby when you retire.
We decided to pursue the least dangerous strategy.
4) to proceed along:
The salmon pursue a course up the river.
The helicopter pursued a western course.
5) to haunt:
Even long after the war he was still pursued by horrible memories.
He was pursued by a fear of being buried alive.
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