Topics

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

An integer m is said to be related to another integer n, if m is a multiple of n, Then the relation is:

A) reflexive and symmetric
B) reflexive and transitive
C) symmetric and transitive
D) equivalence relation

Correct Answer:


B) reflexive and transitive

Description for Correct answer:
\( \Large \frac{n}{n} => n\ R\ n \)

\( \Large n\ R\ n\ A\ n =z \)

=> R is relexive \( \Large \frac{m}{n} => m\ R\ n\ but\ n\ R\ m\ if\ not\ posxsible \)

Therefore, R is not symmetric

For any integer m, n and p, we have

For any integer m, n and p, we have

Now \( \Large \frac{m}{n},\ \frac{n}{p} => m\ R\ n\ and\ n\ R\ p \)

\( \Large \therefore m\ R\ p \forall \ m,\ n,\ p\ \epsilon\ z \)

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

Comments

Similar Questions

1). Which of the following is a null set?

A). \( \Large \{ x : |x| < 1,\ x\ \epsilon\ N \} \)

B). \( \Large \{ x : |x| = 5,\ x\ \epsilon\ N \} \)

C). \( \Large \{ x : x^{2} = 1,\ \epsilon\ Z \} \)

D). \( \Large \{ x : x^{2}+2x+1=0,\ x\ \epsilon\ R \} \)

2). A set contains n elements. Then the power set contains:

A). \( \Large n^{2} elements \)

B). n elements

C). \( \Large \left(2^{n}-1\right) elements \)

D). \( \Large 2^{n} elements \)

3). In what ratio must a mixture of 20% alcohol be mixed with another mixture of 50% alcohol so that the resultant mixture contains 40% alcohol?

A). 3:5

B). 2:6

C). 1:2

D). 3:7

4). 10 litres of 100% pure Methyl alcohol is added to a 5 litre solution containing 40% Methyl alcohol. What is the strength of Methyl alcohol in the resultant mixture?

A). 60%

B). 70%

C). 50%

D). 80%

5). A money lender lends a total of Rs.1000 to two of his customers on Monday. To one of them he charges interest at the rate of 10% p.a. and to the other he charges interest at the rate of 15% p.a. If the average rate of interest earned from the two customers is11.5% p.a.. then how much did he lend to the customer who pays him interest at the rate of 15% p.a.?

A). Rs.200

B). Rs.400

C). Rs.100

D). Rs.300

6). How many kilograms of salt at Rs.50 / Kg must be mixed with 40 Kgs. of salt that costs Rs.35 / Kg so that a merchant will get 20% by selling the mixture at Rs.48 / Kg?

A). 30 Kgs.

B). 25 Kgs.

C). 20 Kgs.

D). 15 Kgs.

7). A mixture of 50 liters of milk and water containing 20% water is further diluted with water so that the mixture has 30% water in it. How many liters of water are to be added?

A). 9.28

B). 7.14

C). 3.35

D). 6.42

8). Two liquids are mixed in the ratio 3 : 2 and the mixture is sold at Rs.11 per liter at a profit of 10%. If the first liquid costs Rs.2 per liter more than the second one, what are the costs of the two liquids?

A). Rs.12.40 & Rs.10.40

B). Rs.16.80 & Rs.14.80

C). Rs.10.80 & Rs.8.80

D). Rs.9.70 & Rs.7.70

9). Two equal containers filled with mixtures of milk and water in the ratio of 4: 1 and 1: 3 respectively were emptied into a larger container. What is the ratio of milk and Water in the larger container?

A). 21 : 19

B). 30 : 10

C). 25 : 15

D). 35 : 5

10). Fresh fruits contain 72% water by weight and dry fruits contain 20% water by weight. How many Kgs. of dry fruits can be obtained from 100 Kgs. of fresh fruits?

A). 40 Kgs

B). 60 Kgs

C). 70 Kgs

D). 35 Kgs