NIMCET 2015 — Mathematics PYQ

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Question

NIMCET 2015 — Mathematics PYQ

NIMCET | Mathematics | 2015

A professor has 24 text books on computer science and is concerned about their coverage of the topics $(P)$ compilers, $(Q)$ data structures and $(R)$ operating systems. The following data gives the number of books that contain material on these topics : $n(P) = 8, n(Q) = 13, n(R) = 13, n(P \cap Q) = 3, n(P \cap Q \cap R) = 2$ , where $n(x)$ is the cardinality of the set $x$ , then, the number of text books that have no material on compiler is:

Choose the correct answer:

Explanation

1. Identify the given values:

Total number of books (Universal Set $U$ ): $n(U) = 24$
Books on Compilers: $n(P) = 8$
Books on Data Structures: $n(Q) = 13$
Books on Operating Systems: $n(R) = 13$
Books on both Compilers and Data Structures: $n(P \cap Q) = 3$
Books on all three topics: $n(P \cap Q \cap R) = 2$

2. Analyze the requirement:

The question specifically asks for the number of textbooks that have no material on compilers.

In set notation, the set of books containing material on compilers is represented by $P$ . Therefore, the set of books with no material on compilers is the complement of $P$ , denoted as $P'$ .

3. Calculate the result:

The formula for the complement of a set is:

n(P') = n(U) - n(P)

Substituting the given values:

n(P') = 24 - 8

n(P') = 16