Mathbee CBSE Mathbee · CBSE Class 12 Maths
Class 12 Relations And Functions · Mcq Single Correct1 Markstypes_of_relations

Class 12 Maths · Relations And Functions · Mcq Single Correct #28

A family has exactly three children: two brothers \(B_1,B_2\) and their sister \(S\). On \(A=\{B_1,B_2,S\}\), define \(xRy\) to mean that \(x\) is a brother of \(y\), with no child considered their own brother. Which property does \(R\) have?

✅ Step-by-Step Solution

Final Answer: Option (D): None of these
  1. The relation is \(\{(B_1,B_2),(B_1,S),(B_2,B_1),(B_2,S)\}\). It is not reflexive. It is not symmetric because \(B_1RS\), but not \(SRB_1\). It is not transitive because \(B_1RB_2\) and \(B_2RB_1\), but not \(B_1RB_1\). Thus none of the three listed properties holds.

Master Chapter 1: Relations And Functions

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Relations And Functions.
📘 Chapter Notes & All Exercises 🚀 Open Interactive Workspace →
← Previous Question
The relation \(R=\{(1,1),(2,2),(3,3)\}\) on the set \(\{1,2,3\}\) is
Next Question →
Let \(A\) be a nonempty set. On \(\mathcal{P}(A)\), define \(XRY\iff…

More Practice Questions in Relations And Functions

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38Q39Q40

Related Questions in Relations And Functions

Class 12 Relations And Functions · Mcq Single Correct
Given the relation \(R=\{(1,2),(2,3)\}\) on the set \(A=\{1,2,3\}\), the minimum number of…
Class 12 Relations And Functions · Mcq Single Correct
The function \(f:\mathbb{R}\to\mathbb{R}\) defined by \(f(x)=e^x\) is
Class 12 Relations And Functions · Mcq Single Correct
If \(f:\mathbb{R}\to\mathbb{R}\)…
Class 12 Relations And Functions · Mcq Single Correct
If \(f:\mathbb{R}\to S\), defined by \(f(x)=\sin x-\sqrt{3}\cos x+1\), is onto, then the…
Class 12 Relations And Functions · Mcq Single Correct
Let \(A=\{1,2,3\}\) and \(B=\{a,b,c\}\). Then the number of bijective functions from \(A\) to…
Class 12 Relations And Functions · Mcq Single Correct
Let \(A\) and \(B\) be two finite sets having \(m\) and \(n\) elements respectively. Then the…