In a class of 300 students, 242 take math, 208 take science, and 183 take both math and science. How many students take neither math nor science?

1 Answer
Aug 11, 2016

3333 students take neither of the subjects.

Explanation:

We will use the formulas (1) : n(AuuB)=n(A)+n(B)-n(AnnB)(1):n(AB)=n(A)+n(B)n(AB),

(2) : n(A-AnnB) =n(A)-n(AnnB)(2):n(AAB)=n(A)n(AB).

(3) : (AuuB)'=A'nnB'...............[De'Morgan's law].

where, A & B sub U and, n(A) denotes the Number of Elements in a Set A sub U, the Universal Set .

Let M= The Set of students taking Maths. , and, S that of

students taking Sc.. Hence, MnnS is the set of students taking both the subjects, whereas, M'nnS' is the set of students opting neither of the subjects.

Our goal is to find n(M'nnS')=n((MuuS)'), because of (3).

Now, let us observe that, (M-MnnS)uu(MnnS)=M and, their intersection is phi, so, by (1), we get,

n(M)=n(M-MnnS)+n(MnnS), i.e.,

242=n(M-MnnS)+183 rArr n(M-MnnS)=59.

(2) rArr n(M)-n(MnnS)=59,

From (1), then, we have,

n(MuuS)=n(M)+n(S)-n(MnnS)=59+208=267

Therefore, n(M'nnS')=n((MuuS)')=n(U-MuuS)

=n(U)-n(MuuS)=300-267=33.

Enjoy Maths.!