Sets, Relations & Functions
Properties of Relation x+y=7
nta_pyq_2023_apr
Grade 11
Question:
Let $A=\{1,2,3,4,5,6,7\}$. The relation $R=\{(x,y)\in A\times A:\ x+y=7\}$ is
an equivalence relation
symmetric but neither reflexive nor transitive
transitive but neither symmetric nor reflexive
reflexive but neither symmetric nor transitive
Step-by-Step Solution
Key Concept: Reflexive requires $(x,x)\in R$: $2x=7$, impossible for integer $x$. Symmetric: if $x+y=7$ then $y+x=7$. ✓. Transitive: $(1,6),(6,1)\in R$ but $(1,1)\notin R$.
Symmetric only.
Correct Answer: 2