Set Theory
Relations
MJMT_Full_Test_07
Grade 12
Question:
Let $R = \{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}$ on set $\{1,2,3\}$. Which properties does $R$ satisfy?
Step-by-Step Solution
Key Concept: Check reflexive: all $(a,a)$ present ✓; symmetric: $(1,2)\in R$ but $(2,1)\notin R$ ✗; transitive: $(1,2),(2,3)\in R$ and $(1,3)\in R$ ✓.
Reflexive: $(1,1),(2,2),(3,3)\in R$ ✓. Symmetric: $(1,2)\in R$ but $(2,1)\notin R$ ✗. Transitive: All compositions check out ✓. Hence reflexive and transitive only.
Correct Answer: 1