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1.Relation and Function
medium
Let $A=\{-4,-3,-2,0,1,3,4\}$ and $R =\{( a , b ) \in A$ $\times A : b =| a |$ or $\left.b ^2= a +1\right\}$ 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 $........$.
A
$5$
B
$7$
C
$6$
D
$4$
(JEE MAIN-2023)
Solution
$R=[(-4,4),(-3,3),(3,-2),(0,1),(0,0),(1,1)$, $(4,4),(3,3)\}$
For reflexive, add $\Rightarrow(-2,-2),(-4,-4),(-3,-3)$
For symmetric, add $\Rightarrow(4,-4),(3,-3),(-2,3),(1,0)$
Standard 12
Mathematics
