Sets, Relations & Functions
Relation on M — Min Elements for Symmetry
nta_pyq_2026_jan
Grade 11
Question:
Let the relation $R$ on the set $M=\{1,2,3,\ldots,16\}$ be given by $R=\{(x,y):4y=5x-3,\,x,y\in M\}$. Then the minimum number of elements required to be added in $R$, in order to make the relation symmetric, is equal to
Step-by-Step Solution
Key Concept: $y=\tfrac{5x-3}{4}$. For $y\in M$ (positive integer): $5x-3\equiv0\pmod4\Rightarrow x\equiv3\pmod4$. So $x=3,7,11,15$.
2 elements to add.
Correct Answer: 3