Among 54 SEE appeared students, 18 got 'A' grade in maths only. 25 got 'A' grade in English only and 7 students didn't get 'A' grade in these two subjects.

(i) Represent the above information in a Venn-diagram.

(ii) Find the number of students who got 'A' grade in both of these subjects.

(iii) How many students got 'A' grade in maths?

Solution:

Let U be the set of total students. Similarly, let M and E be the sets of students who secured 'A' grade in Mathematics and English, respectively.

Given,

$n(U) = 54$

$n_o(M) = 18$

$n_o(E) = 25$

$n( \overline{M \cup E}) = 7$

To find:

(ii) $n(M \cap E) = ?$

(iii) $n(M) = ?$

For (i)

Show the information in a Venn-diagram.

For (ii)

We know,

$n(U) = n_o(M) + n_o(E) + n(M \cap E) + n( \overline{M \cup E})$

$or, 54 = 18 + 25 + n(M \cap E) + 7$

$or, 54 = 43 + 7 + n(M \cap E)$

$or, 54 = 50 + n(M \cap E)$

$or, 54 - 50 = n(M \cap E)$

$\therefore n(M \cap E) = 4$

For (iii)

We know,

$n(M) = n_o(M) + n(M \cap E)$

$or, n(M) = 18 + 4$

$\therefore n(M) = 22$

Hence,

The required number of students who secured 'A' grade in both of these subjects is 4 students and the total number of students who secured 'A' grade in Mathematics is 22.

#SciPiPupil