The solution for all three is mathematically given as
Generally, the equation for students taking only PE and not Bio and Eng is mathematically given as
P(PBE)= 28 – (5+6+4)
= 28 - 15
= 13
Students taking only Bio and not PE and Eng
P(BP)= 31 – (5+4+2)
= 31 - 11
= 20
Students who are merely studying English and are not also taking Bio and PE
P(EP)= 42 – (6+4+2)
= 42 - 12
= 30
Now, students who have taken three different classes
P(3)= 100 - ( 13 + 5 + 4 + 20 + 2 + 30 + 6 )
= 100 - 80
= 20
In conclusion, Students who have taken BIO and PE but not ENG will get a = 5 for their efforts.
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