Let A=-4,-3,-2,0,1,3,4 and R=(a,b) A A:b=|a| or b^2=a+1 be a relation on A.

Question

Let $A={-4,-3,-2,0,1,3,4}$ and $R={(a,b)\in A	imes A:b=|a|$ or ${b}^{2}=a+1}$ be a relation on $A$. Then the minimum number of elements, that must be added to the relation $R$ so that it becomes reflexive and symmetric, is \_\_\_\_\_\_\_\_\_\_

Answer: 7

Accepted Answer

$\begin{gathered} A ={-4,-3,-2,0,1,3,4} \ \ R= {(-4,4),(-3,3),(0,0),(1,1) \ (3,3),(4,4),(0,1),(3,-2)} \end{gathered}$

Relation to be reflexive $(a,a)\in R\foralla\in A$

$\Rightarrow (-4,-4),(-3,-3),(-2,-2)$ also should be added in $R$.

Relation to be symmetric if $(a,b)\in R$, then $(b,a)\in R\foralla,b\in A$

$\Rightarrow (4,-4),(3,-3),(1,0),(-2,3)$ also should be added in $R$

$\Rightarrow$ Minimum number of elements to be added to $R=3+4=7$

Solutions · 1