Everybody in the red circle M have masters.
Everybody in the blue circle C have certification.
a = the number of employees who have a masters but no certification
b = the number of employees who have both a masters and a certification
c = the number of employees who have a certification but no masters
d = the number of employees who have neither a masters nor a
certification
A company has 22 employees.
a+b+c+d = 22
Twelve of these employees have masters degrees
a+b = 12
and fifteen have at least one Microsoft Certification
b+c = 15
and three have neither a Microsoft certification nor a masters
degree.
d = 3
So we have this system of four equations and 4 unknowns:
Solve by substitution or elimination.
Subtract the 2nd equation from the first, get c+d=10.
Substitute d=3, get c=7. Substitute c=7 in b+c=15,
get b=8. Substitute b=8 in a+b=12, get a=4.
How many have both a Masters degree and a certification?
That's b = 8.
Edwin
