Let X be the set of all persons living in a city. Persons x, y in X are said to be related as x < y if y at least 5 years older than x. which one of the following is correct?

This question was previously asked in
NDA (Held On: 19 Apr 2015) Maths Previous Year paper
View all NDA Papers >
  1. The relation is an equivalence relation on X.
  2. The relation is transitive but neither reflexive nor symmetric.
  3. The relation is reflexive but neither transitive nor symmetric.
  4. The relation is symmetric but neither transitive nor reflexive.

Answer (Detailed Solution Below)

Option 2 : The relation is transitive but neither reflexive nor symmetric.
Free
NDA 01/2025: English Subject Test
5.6 K Users
30 Questions 120 Marks 30 Mins

Detailed Solution

Download Solution PDF

Concept:

Let R be a binary relation on a set A.

1. Reflexive: Each element is related to itself.

  • R is reflexive if for all x ∈ A, xRx.


2. Symmetric: If any one element is related to any other element, then the second element is related to the first.

  • R is symmetric if for all x, y ∈ A, if xRy, then yRx.


3. Transitive: If any one element is related to a second and that second element is related to a third, then the first element is related to the third.

  • R is transitive if for all x, y, z ∈ A, if xRy and yRz, then xRz.

 

4. R is an equivalence relation if A is nonempty and R is reflexive, symmetric and transitive.

Calculation:

Given: x < y if y at least 5 years older than x

⇒ y ≥ x + 5

For Reflexive: (x, x) should ∈R for all x ∈ X

Now, x cannot be 5 years older than himself. So the relation is not reflexive.

For Symmetric: If (x, y) ∈ R ⇒(y, x) ∈ R

(x, y) ∈ R ⇒ y is at least 5 years older than x.

(y, x) ∈ R ⇒ x is at least 5 years older than y. This contradicts the above statement. Hence the relation is not symmetric

For Transitive: If (x, y) ∈ R and (y, z) ∈ R ⇒ (x, z) ∈ R.

(x, y) ∈ R ⇒ y is at least 5 years older than x.

(y, z) ∈ R ⇒ z is at least 5 years older than y.

Then, (x, z) ∈ R ⇒ z is at least 5 years older than x.

Since, z is at least 10 years older than x. The relation is transitive.

Latest NDA Updates

Last updated on Jun 18, 2025

->UPSC has extended the UPSC NDA 2 Registration Date till 20th June 2025.

-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.

->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.

-> The selection process for the NDA exam includes a Written Exam and SSB Interview.

-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100. 

-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential. 

Get Free Access Now
Hot Links: teen patti star login teen patti master downloadable content teen patti earning app teen patti tiger