Solution:
We have R={(x,y):|x2−y2|<16}
Let x=1,|x2−y2|<16⇒|1−y2|<16
⇒ |y2−1|<16⇒y=1,2,3,4
Let x=2,|x2−y2|<16⇒|4−y2|<16
⇒ |y2−4|<16⇒y=1,2,3,4
Let x=3,|x2−y2|<16⇒|9−y2|<16
⇒ |y2−9|<16⇒y=1,2,3,4
Let x=4,|x2−y2|<16⇒|16−y2|<16
⇒ |y2−16|<6⇒y=1,2,3,4,5
Let x=5,|x2−y2|<16⇒|25−y2|<16
⇒ |y2−25|<16⇒y=4,5
∴ R={(1,1),(1,2),(1,3), (1,4),(2,1),(2,2),(2,3), (2,4),(3,1),(3,2), (3,3),(3,4),(4,1),(4,2), (4,3),(4,4),(4,5),(5,4), (5,5)}.
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