>> Elementary Mathematics >> Set theory
1). \( \Large A- \left(B \cap C\right) \) is equal to
A). \( \Large \left(A-B\right)\cap \left(A-C\right) \) B). \( \Large \left(A-B\right)\cup \left(A-C\right) \)
C). \( \Large \left(A\cap B\right)-C \) D). None of these
2). If A = \( \Large \{ x : x^{2} = 1 \} \) and B \( \Large \{ x : x^{4} = 1 \} \), then \( \Large A \cup B \) is equal to:
A). {i, -i} B). {-1, 1}
C). {-1, 1, i. -i} D). None of these
3). If A = \( \Large \{ x : x = 4n+1, 2 \le n \le 5 \} \) then number of subsets of A is:
A). 16 B). 15
C). 4 D). none of these
4). Let R and S be two relations on a set A. Then which is not correct?
A). R and S are transitive, then R u S is also transitive. B). R and S are transitive, then R n S is also transitive.
C). R and S are reflexive, then R n S is also reflexive. D). R and S are symmetric, then R U S is also symmetric
5). The group of beautiful girls is:
A). a null set B). a finite set
C). a singleton set D). 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:
A). symmetric and transitive B). reflexive and symmetric
C). a partial order relation D). 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:
A). 6 B). 9
C). 7 D). all of these
8). If \( \Large N_{a}=\{ an : n \epsilon N \} \), then \( \Large N_{3} \cap N_{4} \) is equal to:
A). \( \Large N_{7} \) B). \( \Large N_{12} \)
C). \( \Large N_{3} \) D). \( \Large N_{4} \)
9). The relation "Congruence modulo m" is:
A). reflexive only B). transitive only
C). symmetric only D). an equivalence relation
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:
A). 144 B). 12
C). 24 D). 30