Let
Question:

Let $R=\left\{(x, y):\left|x^{2}-y^{2}\right|<1\right)$ be a relation on set $A=\{1,2,3,4,5\}$. Write $R$ as a set of ordered pairs.

Solution:

R is the set of ordered pairs satisfying the above relation. Also, no two different elements can satisfy the relation; only the same elements can satisfy the given relation.

So, R = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5)}

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