There are 8 types of growers here.

Grower       Growing       Growing          Growing 

type       Raspberries   Blueberries      Strawberries

Type #1         YES           NO           NO

Type #2         YES          YES           NO

Type #3          NO          YES           NO 

Type #4         YES           NO          YES

Type #5         YES          YES          YES

Type #6          NO          YES          YES

Type #7          NO           NO          YES

Type #8          NO           NO           NO

Let's draw three mutually overlapping circles:

Notice that there are 8 regions.

Regions #1, #2, #4, and #5 make up the set R, of raspberry growers.

       Region #1 consists only of those growing raspberries, but who are

       NOT growing blueberries and NOT growing strawberries.

       Region #2 consists only of those growing BOTH raspberries and

       blueberries, but who are NOT growing strawberries.

       Region #3 consists only of those growing blueberries, but who are

       NOT growing raspberries and NOT growing strawberries.

       Region #4 consists only of those growing BOTH raspberries and

       strawberries, but who are NOT growing blueberries.

       Region #5 consists only of those growing ALL THREE kinds of berries. 

       Region #6 consists only of those growing BOTH blueberries and

       strawberries, but who are NOT growing raspberries.

       Region #7 consists only of those growing strawberries, but who are

       NOT growing raspberries and NOT growing blueberries.

       Region #8 consists only of those NOT growing ANY of the 

       kinds of berries.

Let's start with the most inclusive, i.e., those that grew some

of all three types of berries:

>>...9 grew all three types...<<

That's the growers of type #5, so we erase #5 and put 9 in its place:

>>...23 grew both raspberries and blueberries...<<

Regions #2 and #5 grew raspberries and blueberries, and since region #5

has 9 of the 23 already accounted for, the other 23-9 or 14 growers are in

region #2, so erase #2 and put 14 in its place

>>...11 grew both raspberries and strawberries...<<

Regions #4 and #5 grew raspberries and strawberries, and since region #5

has 9 of the 11 already accounted for, the other 11-9 or 2 growers are in

region #4, so erase #4 and put 2 in its place

>>...14 grew both blueberries and strawberries...<<

Regions #5 and #6 grew blueberries and strawberries, and since region #5

has 9 of the 14 already accounted for, the other 14-9 or 5 growers are in

region #6, so erase #6 and put 5 in its place

>>...59 grew raspberries...<<

Regions #1, #2, #5, and #4 grew raspberries, and regions #2, #5, and #4

have respectively 14, 9 and 2 of the 59 already accounted for, so we

add 14+9+2 and get 25 of the 59 already accouted for, that leaves

59-25 or 34 in region #1, so erase #1 and put 34 in its place

>>...50 grew blueberries...<<

Regions #2, #3, #5, and #6 grew raspberries, and regions #2, #5, and #6

have respectively 14, 9 and 5 of the 50 already accounted for, so we

add 14+9+5 and get 28 of the 50 already accouted for, that leaves

50-28 or 22 in region #3, so erase #3 and put 22 in its place

>>...27 grew strawberries...<<

Regions #4, #5, #6, and #7 grew strawberries, and regions #4, #5, and #6

have respectively 2, 9 and 5 of the 27 already accounted for, so we

add 2+9+5 and get 16 of the 27 already accouted for, that leaves

27-16 or 11 in region #7, so erase #7 and put 11 in its place

>>...13 grew none of these three...<<

These 13 are all in region #8, so erase #8 and put 13 in its place

(a)   How many grew only blueberries?

These are in region #3, so the answer is 22

(b)   How many grew both raspberries and blueberries, but not strawberries?

These are in regions #2 and #5, so the answer is 14+9 or 23

(c)   How many grew only raspberries?

These are in region #1, so the answer is 34

(d)   How many grew none of these three or only strawberries?

These are in regions #8 and #1, do the answer is 13+34 or 47.

(e)   How many fruit tree growers were surveyed?

We add the numbers is all the eight regions:

34 + 14 + 22 + 2 + 9 + 5 + 11 + 13 = 110.