A survey of 180 college men was taken. 43 students were in fraternities, 52 participated in campus sports, and 35 participated in campus tutorial programs. 13 participated in fraternities and sports, 14 in sports and tutorial programs, and 12 in fraternities and tutorial programs. 5 participated in all three activities. To start
D) How many participated in fraternities and sports but not in tutorial programs?
E) How many participated in only sports?
(D) 51
(E) 25
Equivalencies??
If A, then B is equivalent to If not B, then not A
Not (A and B) is equivalent to not A OR not B
Not (A or B) is equivalent to not A AND not B
Can you give an equivalent statement to
1. If an Iowa farmer does not grow corn or beans, then he grows alfalfa.
2. It is not true that both Baghdad and Iraq are countries.
3. If my nephew is playing BB tonight, then I am going to the game.
4. If it is cold in Iowa, then I turn up the thermostat.
5. If I crack black walnuts for the bird feeder, then many birds come back often to feed.
6. If the sun does not shine, then Jane does not draw the blinds shut.
7. Either Bob is not sick or Bob is not coughing.
8. It is not true that Alice can run fast and jump high.
To find the answer to question D, we need to calculate the number of individuals who participated in both fraternities and sports but not in tutorial programs.
We can start by noting that there were 43 students in fraternities, 52 students in campus sports, and 35 students in campus tutorial programs.
We know that 13 students participated in both fraternities and sports, and 5 students participated in all three activities.
To find the number of students who participated in fraternities and sports but not in tutorial programs, we must subtract the students who participated in all three activities from those who participated in both fraternities and sports.
Therefore, the number of students who participated in fraternities and sports but not in tutorial programs is:
13 (students in fraternities and sports) - 5 (students in all three activities) = 8 students.
To find the answer to question E, we need to calculate the number of students who participated in only sports.
Since we already know the number of students who participated in both fraternities and sports (13), participated in sports and tutorial programs (14), and participated in all three activities (5), we can subtract these numbers from the total number of students in campus sports (52).
Therefore, the number of students who participated in only sports is:
52 (students in campus sports) - 13 (students in both fraternities and sports) - 14 (students in sports and tutorial programs) - 5 (students in all three activities) = 20 students.
So, 20 students participated in only sports.