Question:
Each student in a class of 40, studies at least one of the subjects English, Mathematics and Economics. 16 study English, 22 Economics and 26 Mathematics, 5 study English and Economics, 14 Mathematics and Economics and 2 study all the three subjects. The number of students who study English and Mathematics but not Economics is
Each student in a class of 40, studies at least one of the subjects English, Mathematics and Economics. 16 study English, 22 Economics and 26 Mathematics, 5 study English and Economics, 14 Mathematics and Economics and 2 study all the three subjects. The number of students who study English and Mathematics but not Economics is
Updated On: Jul 7, 2024
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- 10
- 4
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The Correct Option is B
Solution and Explanation
C stands for set of students taking economics
$a + b + c + d + e + f + g = 40; a + b + d + g = 16$
$b + c + e + g = 22; d + e + f + g = 26$
$b + g = 5; e + g = 14; g = 2$
Go by backward substitution
$e = 12, b = 3, d + f = 12, c + e = 17 \Rightarrow c = 5;$
$a + d = 11$
$a +d + f = 18 \Rightarrow f = 7 \quad \therefore d = 12 - 7 = 5$
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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}
Representation of Sets
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Roster Form: The form in which elements are listed in set. Elements in the set is seperatrd by comma and enclosed within the curly braces.
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Set Builder Form:
- The set builder representation has a certain rule or a statement that specifically describes the common feature of all the elements of a set.
- The set builder form uses a vertical bar in its representation, with a text describing the character of the elements of the set.
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