Set, Relations and FunctionsPYQ Sep 24Question 1949 of 217
All Questions

Let A={1,2,3}\displaystyle A = \{1,2,3\} and consider the relation R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}\displaystyle R = \{(1,1), (2,2), (3,3), (1,2), (2,3), (1,3)\} then R\displaystyle R is

Options

AReflexive but not symmetric
BReflexive but not transitive
CSymmetric and Transitive
DNeither symmetric nor transitive
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — Reflexive but not symmetric

All Options:

  • AReflexive but not symmetric
  • BReflexive but not transitive
  • CSymmetric and Transitive
  • DNeither symmetric nor transitive

Detailed Solution & Explanation

We are given set A={1,2,3}\displaystyle A = \{1,2,3\} and relation R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}\displaystyle R = \{(1,1), (2,2), (3,3), (1,2), (2,3), (1,3)\}.
Let's check the properties of R\displaystyle R:
1. **Reflexive**: For R\displaystyle R to be reflexive, it must contain (1,1),(2,2),(3,3)\displaystyle (1,1), (2,2), (3,3) since A={1,2,3}\displaystyle A = \{1, 2, 3\}.
Since these pairs are in R\displaystyle R, the relation is reflexive.
2. **Symmetric**: For R\displaystyle R to be symmetric, (a,b)∈R  ⟹  (b,a)∈R\displaystyle (a, b) \in R \implies (b, a) \in R.
Here, (1,2)∈R\displaystyle (1, 2) \in R but (2,1)∉R\displaystyle (2, 1) \notin R. Thus, the relation is not symmetric.
3. **Transitive**: For R\displaystyle R to be transitive, (a,b)∈R and (b,c)∈R  ⟹  (a,c)∈R\displaystyle (a, b) \in R \text{ and } (b, c) \in R \implies (a, c) \in R.
Here, (1,2)∈R\displaystyle (1, 2) \in R and (2,3)∈R  ⟹  (1,3)∈R\displaystyle (2, 3) \in R \implies (1, 3) \in R. Thus, the relation is transitive.
Therefore, the relation R\displaystyle R is reflexive but not symmetric.
Hence, **Option A** is the correct answer.

More Questions from Set, Relations and Functions

If A={1,2,3,4,5}\displaystyle A = \{1, 2, 3, 4, 5\}, B={2,4}\displaystyle B = \{2, 4\} and C={1,3,5}\displaystyle C = \{1, 3, 5\} then (A−C)×B\displaystyle (A - C) \times B is:

If f(x)=x2−5\displaystyle f(x)=x^2-5, evaluate f(3)\displaystyle f(3), f(−4)\displaystyle f(-4), f(5)\displaystyle f(5), and f(1)\displaystyle f(1).

Out of a group of 20\displaystyle 20 teachers in a school, 10\displaystyle 10 teach Mathematics, 9\displaystyle 9 teach Physics and 7\displaystyle 7 teach Chemistry. 4\displaystyle 4 teach Mathematics and Physics but none teach both Mathematics and Chemistry. How many teach Chemistry and Physics; how many teach only Physics?

If A={1,2,3,4,5,7,8,9}\displaystyle A = \{1, 2, 3, 4, 5, 7, 8, 9\} and B={2,4,6,7,9}\displaystyle B = \{2, 4, 6, 7, 9\} then how many proper subset of A∩B\displaystyle A \cap B can be created?

The number of subsets of the set {0,1,2,3}\displaystyle \{0, 1, 2, 3\} is:

If f(x)=x2+x−1\displaystyle f(x) = x^2+x-1 and 4f(x)=f(2x)\displaystyle 4f(x) = f(2x), then find the value of 'x'.

Ready to Master Set, Relations and Functions?

Practice all 217 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free