This can be solved using formula for Venn Diagrams:
Total = n(A)+ n(B) - n(both A and B) + n(neither A nor B)
Where, the n in front indicates number of items [ n(A) is number of elements in set A ]
We can take:
- set A as students taking Ethics
- set B as students taking Metaphysics
Given:
Tota = 15,000
n(A) = 2200
n(both A and B) = 1700
n(neither A nor B) = 9500
Substituting these into our formula, we get:
[tex]15,000=2200+n(B)-1700+9500\\15,000=n(B)+10,000\\n(B)=15,000-10,000\\n(B)=5000[/tex]
Hence, 5000 students are taking metaphysics this term.
*** If we want to know students taking metaphysics ONLY, we can subtract n(both A and B) from 5000. So we have [tex]5000-1700=3300[/tex] ***
ANSWER:
Total students taking Metaphysics = 5000
Students taking Metaphysics only = 3300
