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Relation |x²-y²|<16 on {1,2,3,4,5} | JEE Sets and Relations

JEE Maths question with a full step-by-step solution.

Question
The relation RR defined on the set A={1,2,3,4,5}A = \{1, 2, 3, 4, 5\} by R={(x,y):∣x2−y2∣<16}R = \{(x, y) : |x^2 - y^2| < 16\} is given by:
A{(1,1),(2,1),(3,1),(4,1),(2,3)}\{(1, 1), (2, 1), (3, 1), (4, 1), (2, 3)\}
B{(2,2),(3,2),(4,2),(2,4)}\{(2, 2), (3, 2), (4, 2), (2, 4)\}
C{(3,3),(3,4),(5,4),(4,3),(3,1)}\{(3, 3), (3, 4), (5, 4), (4, 3), (3, 1)\}
DNone of thesecorrect
Solution
Test each xx in ∣x2−y2∣<16|x^2 - y^2| < 16:
x=1,2,3:y∈{1,2,3,4}x = 1, 2, 3: \quad y \in \{1, 2, 3, 4\}
x=4:y∈{1,2,3,4,5}x = 4: \quad y \in \{1, 2, 3, 4, 5\}
x=5:y∈{4,5}.x = 5: \quad y \in \{4, 5\}.
 The complete relation has 1919 pairs and matches none of the listed sets. ∴\therefore none of these. Correct answer: (4)
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