Of 30 runners surveyed, 22 go running in the morning and 15 go running in the evening. Seven of the runners surveyed go running in both the morning and the evening. How many runners go running in the morning but not the evening?

By the way I think that the answer is 8. Is it correct?

No.

http://www.jiskha.com/display.cgi?id=1349563160

But still i do not get it! Please explain!

The question asks how many only run in the morning. Since 22 run in the morning and 7 run both times, subtract 7 from 22.

To find out how many runners go running in the morning but not the evening, we need to use the principle of inclusion-exclusion.

First, let's label the following sets:
A = Runners who go running in the morning.
B = Runners who go running in the evening.

We are given that there are 30 runners surveyed, and we want to find the number of runners in set A but not in set B.

Using the principle of inclusion-exclusion, we can write the formula:
|A ∩ B| = |A| + |B| - |A ∪ B|

We are given the following information:
|A| = 22 (22 runners go running in the morning)
|B| = 15 (15 runners go running in the evening)
|A ∩ B| = 7 (7 runners go running in both the morning and the evening)

Now, we can substitute these values into the formula and solve for |A ∪ B| (i.e., the total number of runners who go running either in the morning or in the evening):
7 = 22 + 15 - |A ∪ B|

Rearranging the formula, we find:
|A ∪ B| = 22 + 15 - 7
|A ∪ B| = 30

Therefore, there are 30 runners in total who go running either in the morning or in the evening.

Now, let's find the number of runners who go running in the morning but not the evening:
|A - B| = |A| - |A ∩ B|

Substituting the values we know:
|A - B| = 22 - 7
|A - B| = 15

Therefore, 15 runners go running in the morning but not the evening.