Sets, Relations & Functions
Minimum Elements for Symmetric Relation
nta_pyq_2023_apr
Grade 11
Question:
Let $A=\{0,3,4,6,7,8,9,10\}$ and $R=\{(x,y):\ x-y\text{ is odd positive}\text{ or }x-y=2\}$. Minimum elements to add to $R$ for it to be symmetric is equal to _________
Step-by-Step Solution
Key Concept: The relation $R$ contains 19 ordered pairs $(a,b)$ with $a>b$. For each, the symmetric pair $(b,a)$ must be added.
19 elements to add.
Correct Answer: 19