Question:
Out of $100$ students; $15$ passed in English, $12$ passed in Mathematics, $8$ in Science, $6$ in English and Mathematics, $7$ in Mathematics and Science, $4$ in English and Science; $4$ in all the three passed. Then
(i) The number of students passed in English and Mathematics but not in Science is
(ii) The number of students only passed in Mathematics is
(iii) The number of students passed in more than one subject is
Out of $100$ students; $15$ passed in English, $12$ passed in Mathematics, $8$ in Science, $6$ in English and Mathematics, $7$ in Mathematics and Science, $4$ in English and Science; $4$ in all the three passed. Then
(i) The number of students passed in English and Mathematics but not in Science is
(ii) The number of students only passed in Mathematics is
(iii) The number of students passed in more than one subject is
Updated On: Jul 6, 2022
- a
- b
- c
- d
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The Correct Option is B
Solution and Explanation
Let $U$, $E$, $M$ and $S$ be denote the total number of students, number of students passed in English, Mathematics and Science, respectively.
Here, $n(U) = 100$, $n(E) = 15$, $n(M) = 12$, $n(S) = 8$, $n(E \cap M) = 6$,
$n(M \cap S) = 7$, $n(E \cap S) = 4$ and $n (E \cap M \cap S) = 4$
(i) $\therefore$ The number of students passed in English and Mathematics but not in Science
$= n ( E \cap M \cap \bar{S})$
$= n(E \cap M) - n(E \cap M \cap S) = 6 - 4 = 2$
(ii) The number of students only passed in Mathematics
$= n(M \cap \bar{E} \cap \bar{S})$
$= n(M) - n(M \cap E) - n(M \cap S) + n(M \cap E \cap S)$
$= 1 2 -6 -7 + 4 = 16-13 = 3$
(iii) The number of students passed in more than one subject
$= n(M \cap E) + n(M \cap S ) + n(S \cap E) - 2n(M \cap E \cap S)$
$= 6 + 7 + 4 - 2(4) = 17-8 = 9$
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Concepts Used:
Sets
Set is the collection of well defined objects. Sets are represented by capital letters, eg. A={}. Sets are composed of elements which could be numbers, letters, shapes, etc.
Example of set: Set of vowels A={a,e,i,o,u}
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Set Builder Form:
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