Sets, subsets and venn diagrams?

Question

suppose that a sample of 100 students were surveyed to find out which they read of the magazines times, newsweek and bulletin. it was found that
55 students read at least one of the above magazines.
28 read time,
26 read newsweek
14 read bulletin.
4 read both time and bulletin,
3 read both newsweek and bulletin and
2 read all three magazines.

a) how many students read none of the above 3 magazines?

b) how many students read times and newsweek?

c) how many students read newsweek but neither of the other 2?

so far there are 3 different answers does anyone no which is actually correct?

Answer 1

A= 100- 55 = 45
B set up a Venn diagram and you will be able to figure out the answer is 2
C set up a Venn diagram and you will be able to figure out the answer is 19
hope this helps

Answer 2

construct a venn diagram:
let
T=times
N=newsweek
B=bulletin
with intersection of all is 2 (reads all)
so intersection of T and N - B = x
intersection of N and B - T = 1
intersection of T and B - N = 2
students who reads T only = 28 - 4 - x = 24 - x
students who reads N only = 26 - 3 - x = 23 - x
students who reads B only = 14 - 5 = 9.
students who does not read any of the three = 45
students who reads at least one is 55
a) students who reads none of the three 100 - 55= 45 //

b) first solve for x by adding all then equate to 55
55 = 24 - x + 23 - x +9 + 2 + 1 + x + 2
55 = 61 - x
x = 6.
Note: "and" means both so intersection of T and N, that is
x + 2 = 6 + 2 = 8 //

c)that is 23 - x = 23 - 6 = 17 // answer

Answer 3

magazine time =a
newsweek =b
bulletin =c
na=28
nb=26
nc=14
a^c=4
b^c=3
a^b^c=2

a)100-aUbUc=100-55=45

b)aubuc=na+nb+nc- a^b-a^c-b^c+a^b^c
55=28+26+14-4-3+2-a^b
a^b=8
8 students read both times and newsweek

c)nb-a^b-b^c-a^b^c=26-8-2-3=13 read only newsweek