Question

among all athletes (denoted by ( a )), there are those who play golf. there are also those athletes (denoted by ( w )) who have won a tournament competition. golfers are made up of professionals (denoted by ( pg )) and amateurs (denoted by ( ag )). represent, by shading the appropriate region(s), all athletes who are either professional golfers who have won a tournament or amateur golfers who have not.

Explanation:

Step1: Analyze the first part

Professional golfers who have won a tournament: This is the intersection of \(PG\) and \(W\).

Step2: Analyze the second part

Amateur golfers who have not won a tournament: This is the part of \(AG\) that does not overlap with \(W\).

Step3: Combine the two parts

Since it is an "or" condition, we shade the region that is either the intersection of \(PG\) and \(W\) or the non - overlapping part of \(AG\) with \(W\).

Answer:

Shade the intersection of \(PG\) and \(W\) and the part of \(AG\) that does not overlap with \(W\).