Topics

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

The relation "Congruence modulo m" is:

A) reflexive only
B) transitive only
C) symmetric only
D) an equivalence relation

Correct Answer:




D) an equivalence relation

Description for Correct answer:
\( \Large x=3 \left(mod\ 7\right) => x-3 = 7p,\ \left(p\ \epsilon\ I\right) \)

=> \( \Large x=7p+3,\ p\ \epsilon\ I\ i.e.,\ \{ 7p+3 : p\ \epsilon\ z \} \)

Therefore, Solution set of x is \( \Large \{ 7p + 3 : p\ \epsilon\ I \} \).

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

Comments

Similar Questions

1). 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

2). 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

3). 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

4). Let \( \Large f:N \rightarrow R:f \left(x\right)=\frac{ \left(2x-1\right) }{2} \) and \( \Large g:Q \rightarrow R:g \left(x\right)=x+2 \) be two functions then \( \Large \left(gof\right) \left(\frac{3}{2}\right) \)

A). 3

B). 1

C). \( \Large \frac{7}{2} \)

D). None of these

5). If N be the set of all natural numbers, consider \( \Large f:N \rightarrow N:f \left(x\right)=2x \forall x \epsilon N \), then f is:

A). one-one onto

B). one-one into

C). many-one

D). one of these

6). N is the set of natural numbers. The relation R is defined on \( \Large N \times N \) as follows: \( \Large \left(a,\ b\right)R \left(c,\ d\right) \Leftrightarrow a+d=b+c \) is:

A). reflexive

B). symmetric

C). transitive

D). all of these

7). Let \( \Large A = \{ 2,\ 3,\ 4,\ 5 \} \) and
\( \Large R = \{ \left(2,\ 2\right),\ \left(3,\ 3\right),\ \left(4,\ 4\right),\ \left(5,\ 5\right),\
\left(2,\ 3\right),\ \left(3,\ 2\right),\) \( \Large \ \left(3,\ 5\right),\ \left(5,\ 3\right) \} \) be a relation in A, Then R is:

A). reflexive and transitive

B). reflexive and symmetric

C). reflexive and anti-symmetric

D). none of the above

8). For real numbers x and y, we write
\( \Large x R y \Leftrightarrow x^{2}-y^{2}+\sqrt{3} \)
is an irrational number. Then the relation R is:

A). reflexive

B). symmetric

C). transitive

D). none of these

9). \( \Large f \left(x\right)=\frac{1}{2}-\tan \frac{ \pi x}{2},\ -1 < x < 1\ and\ g \left(x\right) \) \( \Large =\sqrt{ \left(3+4x-4x^{2}\right) } \) then dom \( \Large \left(f + g\right) \) is given by:

A). \( \Large \left[ \frac{1}{2}, 1 \right] \)

B). \( \Large \left[ \frac{1}{2}, -1 \right] \)

C). \( \Large \left[ -\frac{1}{2}, 1 \right] \)

D). \( \Large \left[ -\frac{1}{2}, -1 \right] \)

10). If \( \Large R \subset A \times B\ and\ S \subset B \times C \) be two relations, then \( \Large \left(SOR\right)^{-1} \) is equal to:

A). \( \Large S^{-1}OR^{-1} \)

B). \( \Large R^{-1}OS^{-1} \)

C). SOR

D). ROS