Verified Solution • 2025–26 Session moderate

QJEEM23Ma3ae0: JEE Main 2023 Mathematics - Class 11 JEEM23Ma3ae0 Solution: Let and or be a relation on . Then the minimum number of…

Let A={−4,−3,−2,0,1,3,4}\mathrm{A}=\{-4,-3,-2,0,1,3,4\} and R={(a,b)∈A×A:b=∣a∣\mathrm{R}=\left\{(a, b) \in \mathrm{A} \times \mathrm{A}: b=|a|\right. or b2=a+1}\left.b^{2}=a+1\right\} be a relation on A\mathrm{A} . Then the minimum number of elements, that must be added to the relation R\mathrm{R} so that it becomes reflexive and symmetric, is __________

Step-by-Step Verified Solution

Aamp;={−4,−3,−2,0,1,3,4}R=amp;{(−4,4),(−3,3),(0,0),(1,1)amp;(3,3),(4,4),(0,1),(3,−2)}\begin{aligned}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{aligned}

Relation to be reflexive (a,a)∈R∀a∈A(a, a) \in R \forall a \in A

⇒(−4,−4),(−3,−3),(−2,−2)\Rightarrow (-4,-4),(-3,-3),(-2,-2) also should be added in RR .

Relation to be symmetric if (a,b)∈R(a, b) \in R , then (b,a)∈R∀a,b∈A(b, a) \in R \forall a, b \in A

⇒(4,−4),(3,−3),(1,0),(−2,3)\Rightarrow (4,-4),(3,-3),(1,0),(-2,3) also should be added in RR

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

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