In a fraternity with 38 members , 18 take math, 5 take both math and literature and 8 take neither math or literature. how many take literature but not math?
I came up with 16 is that correct or am i lost ?
I got 12
Make a Venn diagram consisting of two intersecting circles, one called M, the other called L
Put a rectangle around the circles.
place 5 in the intersection of M and L
since M contains 18 , but 5 are already written down, place 13 in the M only part of the circle.
place x in the L only part of L
place 8 in the rectangle outside the two circles
Now 13+5+x+8 = 38
x = 12
To find the number of members who take literature but not math, you can use the principle of inclusion-exclusion. Here's how you can approach the problem step by step:
1. Start with the total number of fraternity members: 38.
2. Deduct the number of members who take neither math nor literature: 8.
So, the remaining number of members who take either math, literature, or both is: 38 - 8 = 30.
3. Deduct the number of members who take both math and literature: 5.
Now, the number of members who take either math or literature (or both) but not both is: 30 - 5 = 25.
4. Subtract the number of members who take math from the previous result: 25 - 18 = 7.
This gives you the number of members who take literature but not math.
Therefore, according to the given information, 7 members take literature only, without taking math.