Class 12 Relations And Functions · Short Answer2 Markstypes_of_relations
Class 12 Maths · Relations And Functions · Short Answer #209
On A={0,1,2,3}, test R={(0,0),(0,1),(0,3),(1,0),(1,1),(2,2),(3,0),(3,3)} for the three relation properties.
✅ Step-by-Step Solution
Final Answer: Reflexive and symmetric, not transitive.
- All four diagonal pairs occur, so R is reflexive.
- The off-diagonal pairs occur with their reversals, proving symmetry. But (1,0),(0,3) occur while (1,3) does not, disproving transitivity.
- Therefore R is reflexive and symmetric but not transitive.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] All four diagonal pairs occur, so R is reflexive.
- [1 mark] The off-diagonal pairs occur with their reversals, proving symmetry. But (1,0),(0,3) occur while (1,3) does not, disproving transitivity.
- [0.5 marks] Therefore R is reflexive and symmetric but not transitive.
Master Chapter 1: Relations And Functions
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Relations And Functions.
← Previous Question
For A={1,2,3,4,5}, list R={(a,b)∈A²:|a²−b²|<8}.
Next Question →On R define aRb iff a−b+√2 is irrational. Test reflexivity, symmetry…
More Practice Questions in Relations And Functions
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…