[4 marks sum]

Question 14 Marks

In a class there are 27 students. Out of these 14 study Psychology and 19 study Geography. There are 11 students who study both Psychology and Geography.
Q.1. How many students study Psychology but not Geography?
(a) 3 (b) 4 (c) 5 (d) 6
Q.2. How many students study Geography but not Psychology?
(a) 7 (b) 8 (c) 9 (d) 11
Q.3. How many students study neither Psychology nor Geography?
(a) 8 (b) 7 (c) 6 (d) 5
Q.4. What is the difference between the number of students who study Psychology only and those who study Geography only?
(a) (b) 5 (c) 6 (d) 7

Answer

Ans.1. (A)
Ans.2. (B)
Ans.3. (D)
Ans.4. (B)

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Question 24 Marks

Sid is given a few sets. These are represented as A, B, C, D, E, F and G on a plain sheet of paper as a Venn Diagram.

Q.1. How many empty sets are there in the given Venn Diagram?
(α) 3 (b) 2 (c) 1 (d) 0
Q.2. How many singleton sets are there in the given Venn Diagram ?
(α) 0 (b) 1 (c) 2 (d) 3
Q.3. How many pairs of equivalent sets are there in the given Venn Diagram ?
(a) 1 (b) 2 (c) 3 (d) 4
Q.4. How many pairs of equal sets are there in the given Venn Diagram ?
(α) 0 (b) 1 (c) 2 (d) 3

Answer

Ans.1. (D)
Ans.2. (C)
Ans.3. (B)
Ans.4. (B)

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Question 34 Marks

Let $\mathrm{U}=\{1,2,3,4,5,6,7,8,9,10\}$ be the universal set and let $A=\{2,3,4,5,6\}$ and $B=\{3,5,7,8\}$ be its subsets.
Find: (i) $\mathrm{A}^{\prime}$ (ii) $\mathrm{B}^{\prime}$ (iii) $\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}$ (iv) $\mathrm{A}^{\prime} \cup \mathrm{B}^{\prime}$
Verify that: (v) $(\mathrm{A} \cup \mathrm{B})^{\prime}=\left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}\right)$, (vi) $(\mathrm{A} \cap \mathrm{B})^{\prime}=\left(\mathrm{A}^{\prime} \cup \mathrm{B}^{\prime}\right)$

Answer

(i) $\mathrm{A}^{\prime}=\{1,7,8,9,10\}$
$\mathrm{B}^{\prime}=\{1,2,4,6,9,10\}$
(iii) $\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}=\{1,9,10\}$
(iv) $\mathrm{A}^{\prime} \cup \mathrm{B}^{\prime}=\{1,2,4,6,7,8,9,10\}$

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MATHS [4 marks sum]

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