Steve answered this a few hours ago.
http://www.jiskha.com/display.cgi?id=1344612969
D) How many participated in fraternities and sports but not in tutorial programs?
E) How many participated in only sports?
http://www.jiskha.com/display.cgi?id=1344612969
1. Start by finding the total number of participants in fraternities and sports, which is given by the intersection of the two sets:
Fraternities and sports = 13 participants
2. Subtract the number of participants who were in all three activities since they are already counted in the previous step:
Fraternities, sports, and tutorial programs = 5 participants
3. Finally, subtract the number of participants who were in all three activities from the total number of participants in fraternities and sports:
Fraternities and sports but not in tutorial programs = 13 - 5 = 8 participants.
Therefore, 8 participants participated in fraternities and sports but not in tutorial programs.
To find the number of participants who participated in only sports, you can use the following steps:
1. Start by finding the total number of participants in sports, which is 52.
2. Subtract the number of participants who were in fraternities and sports, as they are already counted in the previous step:
Fraternities and sports = 13 participants
3. Subtract the number of participants who were in all three activities since they are already counted in the previous step:
Fraternities, sports, and tutorial programs = 5 participants
4. Finally, subtract the number of participants who were in fraternities and sports and those who were in all three activities from the total number of participants in sports:
Only sports = 52 - 13 - 5 = 34 participants.
Therefore, 34 participants participated in only sports.