posted by generose .
In a class of 50 students it was found 21 are taking English
14 are taking Math
28 are taking History
7 are taking Math and English
10 are taking Math and
11 are taking History and English
3 are taking all three courses
1.)Make a Venn Diagram summarizing these data?
2.)ans. the ff.
1.)taking English only?
2.)taking Math or History?
3.)taking Math only?
4.)taking Math and History but not English?
5.)taking English and Math but not History?
6.)taking atleast one of the three course?
7.)taking neither Math nor History?
8.)taking at most two course?
9.)not taking of the three coursr?
10.)taking Math and History?
Use Venn diagrams and this becomes quite easy.
Start with the intersection of the three circles and place 3 in that regions.
Now working from the inside out, enter the data
Make sure you don't count items more than once.
e.g. for the 10 taking Math and History, remember you already have 3 of those accounted for. So in the region showing ONLY Math and History, place 10-3 or 7
repeat for the remaining two doubles.
Now look at the entire circles,
e.g. the Math circle. Notice that there are already entries in that circle, so make sure you enter only the remaining count from the original 14 in the region showing ONLY Math.
Add up all the entries and compare that sum with 50
If the total is less than 50, it would show those students not taking any of the 3 subjects
Once you have entered all the data, all your questions can be easily determined.