Let A = - 4, - 3, - 2, 0, 1, 3, 4 and R = \ ( a, b ) ∈ A × A : b =...

Given,

A = { - 4, - 3, - 2, 0, 1, 3, 4 } and $R = \{ ( a, b ) \in A \times A : b = | a |\text{ or } {b}^{2} = a + 1\}$ be a relation on $A$,

So, the relation is given by,

$R = { ( - 4, 4 ) , ( - 3, 3 ) , ( 0, 0 ) , ( 1, 1 ) , ( 3, 3 ) , ( 4, 4 ) , ( 0, 1 ) , ( 3, - 2 ) }$

Now, relation to be reflexive $( a, a ) \in R \forall a \in A$

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

Now relation to be symmetric if $( a, b ) \in R$, then $( b, a ) \in R \forall a, b \in A$

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

Hence, minimum number of elements to be added to
R = 3 + 4 = 7