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1.Set Theory
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A class has $175$ students. The following data shows the number of students obtaining one or more subjects. Mathematics $100$, Physics $70$, Chemistry $40$; Mathematics and Physics $30$, Mathematics and Chemistry $28$, Physics and Chemistry $23$; Mathematics, Physics and Chemistry $18$. How many students have offered Mathematics alone
A
$35$
B
$48$
C
$60$
D
$22$
Solution

(c) $n(M\ alone)$$ = n(M) – n(M \cap C) – n(M \cap P) + n(M \cap P \cap C)$
$ = 100 – 28 – 30 + 18 = 60$.
Standard 11
Mathematics
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