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Relation aRb if |a²-b²|≤5 on {1,2,3}: False Statement | JEE

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Question
The relation RR is defined in A={1,2,3}A = \{1, 2, 3\} by aRbaRb if ∣a2−b2∣≤5|a^2 - b^2| \le 5. Which of the following is false?
AR={(1,1),(2,2),(3,3),(2,1),(1,2),(2,3),(3,2)}R = \{(1, 1), (2, 2), (3, 3), (2, 1), (1, 2), (2, 3), (3, 2)\}
BR−1=RR^{-1} = R
CDomain of R={1,2,3}R = \{1, 2, 3\}
DRange of R={5}R = \{5\}correct
Solution
Step 1: Test each a∈{1,2,3}a \in \{1, 2, 3\} in ∣a2−b2∣≤5|a^2 - b^2| \le 5.
a=1:∣1−b2∣≤5⇒b=1,2a = 1: \quad |1 - b^2| \le 5 \Rightarrow b = 1, 2
a=2:∣4−b2∣≤5⇒b=1,2,3a = 2: \quad |4 - b^2| \le 5 \Rightarrow b = 1, 2, 3
a=3:∣9−b2∣≤5⇒b=2,3a = 3: \quad |9 - b^2| \le 5 \Rightarrow b = 2, 3
∴R={(1,1),(1,2),(2,1),(2,2),(2,3),(3,2),(3,3)}.\therefore R = \{(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 2), (3, 3)\}.
 Step 2: The condition ∣a2−b2∣|a^2 - b^2| is unchanged on swapping a,b⇒R−1=Ra, b \Rightarrow R^{-1} = R.
Domain={1,2,3},Range={1,2,3}.\text{Domain} = \{1, 2, 3\}, \qquad \text{Range} = \{1, 2, 3\}.
 ∴\therefore the statement "Range of R={5}R = \{5\}" is false. Correct answer: (4)
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