The relation R on the set A = 1, 2, 3 defined by R = (1,1), (2,2), (3,3), (1,3), (2,3), (1,2) is Option 1: reflexive but neither symmetric nor transitive Option 2: reflexive and transitive Option 3: reflexive and symmetric Option 4: an equivalence relation

Answer: reflexive and transitive. Solution: All of (1,1),(2,2),(3,3) are present, so R is reflexive. (1,3) R but (3,1) R, so it is not symmetric, and therefore not an equivalence relation. The only chain to test is (1,2) and (2,3), and (1,3) R, so R is transitive.

Algebra

Relations & Functions

Easy

core

The relation R on the set A = {1, 2, 3} defined by R = {(1,1), (2,2), (3,3), (1,3), (2,3), (1,2)} is

reflexive but neither symmetric nor transitive

reflexive and transitive

reflexive and symmetric

an equivalence relation

✅ Correct Option: 2

All of $(1,1),(2,2),(3,3)$ are present, so $R$ is reflexive.

$(1,3)\in R$ but $(3,1)\notin R$ , so it is not symmetric, and therefore not an equivalence relation.

The only chain to test is $(1,2)$ and $(2,3)$ , and $(1,3)\in R$ , so $R$ is transitive.

2026: 18 May Shift 2

For the relation R defined below, where $\mathbb{R}$ and N denotes set of real numbers and set of natural numbers respectively, Match the LIST-I with LIST-II

LIST-I Relation	LIST-II Properties of relation hold by R
A. $R=\{(a,b): a,b\in \mathbb{R}; a^2+b^2=4\}$	I. Neither reflexive, nor symmetric, nor transitive
B. $R=\{(a,b): a,b\in \mathbb{R}; 1+ab>0\}$	II. Equivalence relation
C. $R=\{(a,b): a,b\in N; a+2b=8\}$	III. Symmetric but neither reflexive nor transitive
D. On N×N, relation R defined by $(a,b)R(c,d) \Leftrightarrow a+d=b+c$	IV. Reflexive and symmetric, but not transitive

Choose the correct answer from the options given below:

2026: 21 May Shift 1

If $A = R - \{2\}$ and $B = R - \{1\}$ and function $f: A \rightarrow B$ defined by $f(x) = \frac{x-1}{x-2}$ , then $f$ is

2025: 3 June Shift 2

The relation R on the set of real numbers defined by $R = \{(a, b): a \leq b^2\}$ is

2025: 22 May Shift 2

The graph given below represents which of the following function?

2025: 13 May Shift 1

Let $A = \{a, b, c\}$ . Then number of relations containing $(a,b)$ and $(b, c)$ which are reflexive and transitive but not symmetric is

2022: 7 Aug Shift 2

Let L be the set of all lines in a plane and R be the relation in L defined as $R = \{(l_1, l_2) : l_1 \text{ is perpendicular to } l_2, \text{ where } l_1, l_2 \in L\}$ . Choose the correct answer :

The relation R on the set A = {1, 2, 3} defined by R = {(1,1), (2,2), (3,3), (1,3), (2,3), (1,2)} is

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)