Bissoy.com
Doctors Medicines MCQs Q&A

If X = {a, b, c} and R is a relation on X such that R = {(a, a), (b, b), (c, c)}. Then R is a/an ?

If X = {a, b, c} and R is a relation on X such that R = {(a, a), (b, b), (c, c)}. Then R is a/an ? Correct Answer Reflexive, symmetric, transitive and anti-symmetry

Concept:

  • Identity Relation:

Let A be a non-empty set then the relation IA = {(a, a): ∀ a ∈ A} on A is called the identity relation on A.

  • Reflexive:

Let R be a relation on a non-empty set A, if every element of A is related to itself then R is said to be a reflexive relation.

Thus, R is reflexive ⇔ (a, a) ∈ R, ∀ a ∈ A.

  • Symmetric:

Let R be a relation on a non-empty set A, then the relation R is said to be symmetric relation ⇔ (a, b) ∈ R ⇒ (b, a) ∀ a, b ∈ A.

  • Anti–symmetric Relation:

Let R be a relation on a non-empty set A, then the relation R is said to be anti-symmetric

⇔ (a, b) ∈ R and (b, a) ∈ R ⇒ a = b ∀ a, b ∈ A.

  • Transitive:

Let R be a relation on a non-empty set A, then the relation R is said to be transitive relation ⇔ (a, b) ∈ R and (b, c) ∈ R ⇒ (a, c) ∈ R, ∀ a, b, c ∈ A.

  • Equivalence:

Let R be a relation on a non-empty set A, then the relation R is said to be equivalence relation if R is reflexive, symmetric and transitive.

Note:

The identity relation on a non-empty set is always reflexive, symmetric, anti-symmetric and transitive.

Calculation:

Given: X = {a, b, c} and R is a relation on X such that R = {(a, a), (b, b), (c, c)}

As we can see that, (x, x) ∈ R ∀ x ∈ X ⇒ R is an identity relation on X.

We know that, the identity relation on a non-empty set is always reflexive, symmetric, anti-symmetric and transitive.

Related Questions

According to Naiya̅yikas we ascertain the relation of universal concomitance between x and y :  (A) We can determine the relation only if we can determine the relation of essential identity between x and y   (B) By perceiving that in all cases the presence of x is accompanied by the presence of y  (C) We can determine the relation only if we can determine the relation of cause and effect between x and y  (D) By not perceiving any instance where the presence of x is not accompanied by the presence of y or vice-versa.  Choose the correct answer from the options given below : 
In the given question, a part of the sentence is printed in bold. Below the sentence, three alternatives to the bold part are given which may help improve the sentence. Choose the option that reflects the correct use of the phrase in the context of the sentence. In case the given sentence is correct, your answer is (E) i.e. No correction required. At first glance, it seems implausible that such an intricately engineered bio system such as our could have come about merely as a result of random modifications. i. such an intricately engineered bio system as ours ii. such intricately engineered bio system such as our iii. such intricately engineered bio system such as ours
Which among the following type of relations are considered by Nya̅ya system as necessary relation between middle and major terms? (A) Species - species relation  (B) The causal relation  (C) Member - class relation  (D) Species - genus relation  Choose the correct answer from the options given below :
Which of the following constitutes patentable subject matter?
1. A toxin-where such toxin is found on the skin of a previously unknown tree frog of the Amazon basin, which, when administered to patients with a certain cell cancer, causes a substantial reduction in the number of cancerous cells.
2. An idea-where such idea is that there is a mathematical relation among (i) the exposure time of a tumor to a specified alpha-radiation emitting source, (ii) the size of the tumor in cubic centimeters, and (iii) the success rate of the procedure as determined by survival rate at five years
3. Kidney cells-where such cells are found in a certain variety of wild pigs
4. A new laparoscopic surgical technique-where such technique bears improved results in patient cure
Select the correct answer:
Which of the following is not true? Consider a binary relation on a set A has {a, b, c}. a) The smallest reflexive relation is {(a,a) (b,b) (c,c)} b). The largest symmetric relation is {(a,a) (a,b) (a,c) (b,a) (b,b) (b,c) (c,a) (c,b) (c,c) } c). The largest equivalence relation is A x A . d). Number of partaially ordered relations on set A (1,2) is 5.
The question given below consists of a statement, followed by three arguments numbered I, II and III. You have to decide which of the arguments is/are ‘strong’ arguments and which is/are ‘weak’ arguments and accordingly choose your answer from the alternatives given below each question. Statement: India’s telecom watchdog has suggested regulation of all entities dealing with consumer data—devices such as iPhones, operating systems such as Android, browsers like Google’s Chrome and apps such as Facebook, Paytm, Uber or Zomato— by bringing them under licence conditions that apply to telecom service providers until a general data protection law is put in place by the government. Which of the following argument weakens the above statement in the best possible manner? Arguments: I. The Telecom Regulatory Authority of India (Trai) said the framework for protection of personal information is ‘not sufficient’ and that the issue of data ownership, privacy, and security is complex and multi-dimensional. It suggested expanding the ambit of licence conditions governing telcos to all entities handling customer information and empowerment of customers to keep their data secure. II. The telecom watchdog further said that individual users owned their data, or personal information, and entities such as devices were ‘mere custodians’ and do not have primary rights over that information. III. Telcos and internet service providers (ISPs) though welcomed recommendations that sought to bring app makers under the same regulations. However, content providers have been opposed to being brought under more regulation. 
Arson is a crime of intentionally, deliberately and maliciously setting fire to buildings, wildland areas, abandoned homes, vehicles or other property with the intent to cause damage or enjoy the act. It may be distinguished from other causes such as spontaneous combustion, accidental fires (smoking in bed, e.g.) and natural wildfires. Arson often involves someone deliberately burning their own property, or having someone else do it, to collect the insurance. First-degree arson – Burning an occupied structure such as a school or a place where people are normally present. Second-degree arson – Burning an unoccupied building such as an empty barn or an unoccupied house or other structure in order to claim insurance on such property. Third-degree arson – Burning an abandoned building or an abandoned area, such as a field, forest or woods.   Assuming the given information is true, pick the most appropriate option.
Given below are quantities named A,B and C. Based on the given information, you have to determine the relation between the quantities. You should use the given data and your knowledge of mathematics to choose among the possible answer. Quantity A: Tap1 and Tap2 can fill the tank in 16 hours and 25 hours respectively. Both the taps opened together. After some time Tap 1 is closed and after that the tank is filled in 12 hours. In how many hour Tap 1 and 2 work together? Quantity B: Three taps 1, 2, 3 can fill a cistern in 10,14,18 hours respectively. If tap 1 is kept open all the time and tap 2 and 3 is opened alternatively for an hour then find in how many hours the tank will be filled? Quantity C: Two taps 1 and 2 are such that tap 1 fills the tank in 10 hours and tap2 empties it in 20 hours. If tap 1 is opened first and after 5 hours tap 1 is closed and tap 2 is opened, then the tank emptied in x hours and find the value of x?
In the following passage some of the words have been left out. Read the passage carefully and choose the correct answer for the given blank out of the four alternatives.
The nation has been _____as a relatively extensive, territorial relation of nativity. We have further formulated the_____of the nation as a territorially_____, yet bounded, social relation for the generation, transmission, and ____of life. When the nation is a national state, it is also a_____for the protection of life. The nation is often ______by the metaphor of familial relations and, indeed, has sometimes been considered as some kind of_____family. This is understandable because both the nation and the family are relations of_____. Nonetheless, there is an important difference, and to understand this will _____a more detailed examination of the_____ between territory and bonding.
as a territorially_______, yet bounded, social relation
Arrange the following stages in a sequence, such that they result in an ogee curve between two parallel lines AB and CD, such that they are the tangents to the arc. m) Join the adjacent ends B and C with a straight line. n) Divide the line BC into four parts using the points P1, P2, P3. o) Draw lines such that they pass through the points P1, P2, P3, and are perpendicular to the line BC. p) Draw the perpendicular lines through the points B and C such that they cut the lines passing through P1, P3 respectively at E and F. q) With the center E draw an arc BP2 and with center F draw an arc P2C, thus arc BP2C is required ogee curve.