# Set theory Questions and answers

Topics

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
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