Sets, Relations & Functions
Reflexive and Transitive but Not Symmetric Relations
nta_pyq_2023_apr
Grade 11
Question:
On $A=\{1,2,3\}$, relations containing $(1,2)$ and $(2,3)$ which are reflexive and transitive but not symmetric number is _________.
Step-by-Step Solution
Key Concept: Must include $(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)$ for reflexive+transitive. Then choose subset of $\{(2,1),(3,2),(3,1)\}$ not making it symmetric.
4 relations.
Correct Answer: 4