Topics

General Knowledge
General Science
General English
Aptitude
General Computer Science
General Intellingence and Reasoning
Current Affairs
Exams
Elementary Mathematics
English Literature

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

Correct Answer:

A) {i, -i}

Description for Correct answer:
Given that \( \Large A = \{ x:x^{2}=1 \},\ B=\{ x:x^{4}=1 \} \)

=> \( \Large A = \{ -1,\ 1 \},\ B = \{ -1,\ 1,\ -i,\ i \} \)

Now, \( \Large A - B = \phi,\ B-A = \{ -i,\ i \} \)

Therefore, \( \Large \left(A-B\right) \cup \left(B-A\right) = \{ -i,\ i \} \)

Part of solved Set theory questions and answers : >> Elementary Mathematics >> Set theory

Comments

Similar Questions

1). 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

2). 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

3). The group of beautiful girls is:

A). a null set

B). a finite set

C). a singleton set

D). not a set

4). 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

5). 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

6). 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). \( \Large N_{4} \)

7). The relation "Congruence modulo m" is:

A). reflexive only

B). transitive only

C). symmetric only

D). an equivalence relation

8). 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

9). Which of the four statements given below is different from the other?

A). \( \Large f:A \rightarrow B \)

B). \( \Large f:x \rightarrow f \left(x\right) \)

C). f is a mapping from A to B

D). f is a function from A to B

10). Which of the following is correct?

A). \( \Large A \cap B \subset A \cup B \)

B). \( \Large A \cap B \subseteq A \cup B \)

C). \( \Large A \cup B \subset A \cap B \)

D). None of these