1). \( \Large A \left(B \cap C\right) \) is equal to
View Answer Correct Answer: None of these From Venn diagram \( \Large \left(A \cap B\right)^{c} \) = Portion exterior to \( \Large \left(A \cap B\right)^{c} \cap A \) = Portion showing both shadings = AB
 
2). If A = \( \Large \{ x : x^{2} = 1 \} \) and B \( \Large \{ x : x^{4} = 1 \} \), then \( \Large A \cup B \) is equal to:
View Answer Correct Answer: {i, i} Given that \( \Large A = \{ x:x^{2}=1 \},\ B=\{ x:x^{4}=1 \} \) => \( \Large A = \{ 1,\ 1 \},\ B = \{ 1,\ 1,\ i,\ i \} \) Now, \( \Large A  B = \phi,\ BA = \{ i,\ i \} \) Therefore, \( \Large \left(AB\right) \cup \left(BA\right) = \{ i,\ i \} \)
 
3). If A = \( \Large \{ x : x = 4n+1, 2 \le n \le 5 \} \) then number of subsets of A is:
View Answer Correct Answer: 15 Given that \( \Large A = \{ x:x=4n+1;\ 2 \le n \le 5 \} \) Number of elements in set A is 4 , So, number of proper subsets = \( \Large 2^{4}  1 = 15 \).
 
4). Let R and S be two relations on a set A. Then which is not correct?
View Answer Correct Answer: R and S are transitive, then R u S is also transitive. 
 
5). The group of beautiful girls is:
View Answer Correct Answer: not a set Beautiful is relative term so, it is not well defined term. Therefore, it is not a set.
 
6). R is a relation over the set of real numbers and it is given by \( \Large nm \ge 0 \). Then R is:
View Answer Correct Answer: an equivalence relation 
 
7). In a city of 55 students, the number of students studying different subjects are 23 in mathematics, 24 in physics, 19 in chemistry, 12 in mathematics and physics, 9 in mathematics and chemistry, 7 in physics and chemistry and 4 in all the three subjects. The number of students who have taken exactly one subject is:
View Answer Correct Answer: 7 
 
8). If \( \Large N_{a}=\{ an : n \epsilon N \} \), then \( \Large N_{3} \cap N_{4} \) is equal to:
View Answer Correct Answer: \( \Large N_{12} \) Given that \( \Large N_{a}=\{ an:n \epsilon N \} \) \( \Large N_{3} \cap N_{4} = \{ 3,\ 6,\ 9.\ 12,\ 15, ..... \} \cap \{ 4,\ 8,\ 12,\ 16,\ 20, ... \} \) = \( \Large \{ 12,\ 24,\ 36, ... \} = N_{12} \)
 
9). The relation "Congruence modulo m" is:
View Answer Correct Answer: an equivalence relation \( \Large x=3 \left(mod\ 7\right) => x3 = 7p,\ \left(p\ \epsilon\ I\right) \) => \( \Large x=7p+3,\ p\ \epsilon\ I\ i.e.,\ \{ 7p+3 : p\ \epsilon\ z \} \) Therefore, Solution set of x is \( \Large \{ 7p + 3 : p\ \epsilon\ I \} \).
 
10). Set A has 3 elements and set B has 4 elements. The number of injections that can be defined from A to B is:
View Answer Correct Answer: 24 Given that \( \Large n \left(A\right)=3 \) and \( \Large n \left(B\right)=4 \), the number of injections or oneone mapping is given by. \( \Large ^{4}p_{3} \frac{4 !}{ \left(43\right)!}= 4 \times 3 \times 2 \times 1 = 24 \)

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