Let's look at this in a different way. You're asking the computer to:
find all the records using subject heading aged (Set A) 901 records now find all the records using subject heading exercise (Set B) 783 records then find all the records using subject heading diet (Set C) 1,223 records Match all the records and select only those records that contain all three terms 25 records
So you have narrowed your search and reduced the number from thousands to 25 just by using two "AND" operators. AND logic locates each record that has all the subject terms specified.
OR
Let's look at the term "diet." Does that include the concept of nutrition? Perhaps and perhaps not. Maybe we should use either diet or nutrition in our search. How would we do this? Again, using the subject field, put in diet OR nutrition.And the Venn Diagram would look like this:
So while using AND logic will narrow your search, using OR logic will broaden your search.
NOT
You probably won't use this logical operator as often as the previous two, but sometimes it's handy to be able to exclude something. Maybe your search on the aged and exercise brought up a lot of articles relating to physical therapy after surgery or an accident, but you weren't focusing on that particular aspect of exercise. You could use Exercise NOT Therapy.
Here is the Venn diagram:
Thus, the NOT operator narrows your search.