Sets, Relations & Functions
Minimum Additions for Reflexive and Symmetric
nta_pyq_2023_apr
Grade 11
Let $A=\{-4,-3,-2,0,1,3,4\}$ and $R=\{(a,b):\ b=|a|\ \text{or}\ b^2=a+1\}$. Minimum elements to add to make $R$ reflexive and symmetric is
Step-by-Step Solution
Key Concept: Current $R$ has $(-4,4),(-3,3),(0,0),(1,1),(3,3),(4,4),(0,1),(3,-2)$. Need $(a,a)$ for all $a\in A$: add $(-4,-4),(-3,-3),(-2,-2)$ (3 new). For symmetry: add $(4,-4),(3,-3),(1,0),(-2,3)$ (4 new).
7 elements.
Correct Answer: 7