(i) Let A = {5, 6, 7}.
Define a relation R on A as R = {(5, 6), (6, 5)}.
Relation R is not reflexive as (5, 5), (6, 6), (7, 7) ∉ R.
Now, as (5, 6) ∈ R and also (6, 5) ∈ R, R is symmetric.
=> (5, 6), (6, 5) ∈ R, but (5, 5) ∉ R
∴R is not transitive.
Hence, relation R is symmetric but not reflexive or transitive.
(ii) Consider a relation R in R defined as:
R = {(a, b): a < b}
For any a ∈ R, we have (a, a) ∉ R since a cannot be strictly less than a itself. In fact, a = a.
∴ R is not reflexive.
Now,
(1, 2) ∈ R (as 1 < 2)
But, 2 is not less than 1.
∴ (2, 1) ∉ R
∴ R is not symmetric.
Now, let (a, b), (b, c) ∈ R.
⇒ a < b and b < c
⇒ a < c
⇒ (a, c) ∈ R
∴ R is transitive.
Hence, relation R is transitive but not reflexive and symmetric.
(iii) Let A = {4, 6, 8}.
Define a relation R on A as:
A = {(4, 4), (6, 6), (8, 8), (4, 6), (6, 4), (6, 8), (8, 6)}
Relation R is reflexive since for every a ∈ A, (a, a) ∈R i.e., (4, 4), (6, 6), (8, 8)} ∈ R.
Relation R is symmetric since (a, b) ∈ R ⇒ (b, a) ∈ R for all a, b ∈ R.
Relation R is not transitive since (4, 6), (6, 8) ∈ R, but (4, 8) ∉ R.
Hence, relation R is reflexive and symmetric but not transitive.
(iv) Define a relation R in R as:
R = {a, b): a3 ≥ b3}
Clearly (a, a) ∈ R as a3 = a3.
∴ R is reflexive.
Now,
(2, 1) ∈ R (as 23 ≥ 13)
But,
(1, 2) ∉ R (as 13 < 23)
∴ R is not symmetric.
Now,
Let (a, b), (b, c) ∈ R.
⇒ a3 ≥ b3 and b3 ≥ c3
⇒ a3 ≥ c3
⇒ (a, c) ∈ R
∴ R is transitive.
Hence, relation R is reflexive and transitive but not symmetric.
(v) Let A = {−5, −6}.
Define a relation R on A as:
R = {(−5, −6), (−6, −5), (−5, −5)}
Relation R is not reflexive as (−6, −6) ∉ R.
Relation R is symmetric as (−5, −6) ∈ R and (−6, −5}∈R.
It is seen that (−5, −6), (−6, −5) ∈ R. Also, (−5, −5) ∈ R.
∴ The relation R is transitive.
Hence, relation R is symmetric and transitive but not reflexive.
NCERT questions are designed to test your understanding of the concepts and theories discussed in the chapter. Here are some tips to help you answer NCERT questions effectively:
This question is important because it tests key concepts from the NCERT syllabus and is frequently asked in CBSE exams.
This question is based on core NCERT concepts explained in the chapter and should be revised thoroughly before exams.
Students often lose marks by skipping steps, writing incomplete explanations, or misunderstanding keywords used in the question.
(i) Let A = {5, 6, 7}.
Define a relation R on A as R = {(5, 6), (6, 5)}.
Relation R is not reflexive as (5, 5), (6, 6), (7, 7) ∉ R.
Now, as (5, 6) ∈ R and also (6, 5) ∈ R, R is symmetric.
...
Step-by-step explanation:
• (i) Let A = {5, 6, 7}
•
•
• Define a relation R on A as R = {(5, 6), (6, 5)}
•
Stay updated with our latest educational content and study tips
Thirty is when the question starts to get raised and you’re able to do something because you know you have the experience—you know you have the responsibility. Here are some ways to consider the choice based on a realistic assessment without idealizing either aspect. Restlessness is one of those things that appears in your early … Read more
Read More
It’s not about starting over if you took a break to care for children, take care of yourself, be healthy or for any other reason. This is a realistic strategy for the recovery of skills, selection of the right job, and overcoming the resume problem. One year, three years or 10 years of a career … Read more
Read More
There’s no need to score 95% or achieve a JEE/NEET rank. You don’t need to score 95% or rank in JEE/NEET to build a solid career. A candid and pragmatic guide to the routes that actually work for students who have an average mark and what to do when faced with the options. If … Read more
Read More
AI tools, online platforms that are much cheaper than coaching centres and the changing idea of what “structure” even means have upended this argument more in the past two years than in the decade preceding it. Here’s what is really the case for 2026 – and what has actually stayed the same. If you look … Read more
Read More
be a function defined as
. The inverse of f is map g: Range
Student Discussion
Properties of Relation is
A realtion R on set A is reflexive if aRa for all a belongs to A i.e. is (a,a) belongs to R for all a belongs to R => each element a of A is related to itself.
Ex: Let A = {a,b} and R = {(a,a),(a,b),(b,a)} then R is reflexive as aRa belongs to R but it is not reflexive for pair (b,b) does not belongs to R.
ADD NEW COMMENT