As per given question,
(B ? C) = {b, c, e} ? {b, c, f} = {b, c, e, f}
? A × (B ? C) = {a, d} × {b, c, e, f}
= {(a, b), (a, c), (a, e), (a, f), (d, b), (d, c), (d, e), (d, f)} ?...........(1)
Also, (A × B) = {(a, b), (a, c), (a, e), (d, b), (d, c), (d, e)}
and, (A × C) = {(a, b), (a, c), (a, f), (d, b), (d, c), (d, f)} ?............(2)
? (A × B) ? (A × C) = {(a, b), (a, c), (a, e), (a, f), (d, b), (d, c), (d, e), (d, f)}
From (1) and (2), we have
A × (B ? C) = (A × B) ? (A × C).

Let us assume that the N number of people have only TV.
According to question,
? (40 ? P) + P + 10 + 15 + (50 ? P) = 100
? 115 ? 2P + P = 100
? P = 115 ? 100 = 15
? Only TV = 75 ? 15 ? 10 ? 15 = 35

n(A) = Biology students = 72%
n(B) = Mathematics students = 44%
Total students = n(A ? B) = 100%
? 100% = 72% + 44% - n(A ? B) = 116% - n(A ? B)
? n(A ? B) = 16%
? number of students studying both subjects = 40
? Let the total number of students be P
Now, according to the question,
16P/100 = 40
? P = 250

Given in the question,
n(M ? B) = 50, n(M) = 35, n(B) = 37, n(M ? B) =?
use the below formula
n(M ? B) = n(M) + n(B) ? n(M ? B)
We get 50 = 35 + 37 ? n(M ? B)
? n(M ? B) = 35 + 37 ? 50 = 72 ? 50 = 22
? 22 students have opted for both Mathematics and Biology.
Again number of students who have opted for only Mathematics = n(M) ? n(M ? B) = 35 ? 22 = 13.