Let A = 1, 2, 3 and R= (a, b):|a^2-b^2| 5,a, b . Then write R as set of ordered pairs.

We have, A = 1, 2, 3 and R= (a, b):|a^2-b^2| 5,a, b For the elements of the given set A, we find that |1^2-1^2| 5,|2^2-2^2| ,5|3^2-3^2| 5, |1^2-2^2| 5,|2^2-1^2| 5,|2^2-3^2| 5, and |3^2-2^2| 5 = (1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)

Let A = 1, 2, 3 and R= (a, b):|a^2-b^2| 5,a, b . Then write R as …

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Question

Let A = {1, 2, 3} and $\text{R}=\{(\text{a, b}):|\text{a}^2-\text{b}^2|\leq5,\text{a, b}\in\text{A}\}.$ Then write R as set of ordered pairs.

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Answer

We have,
A = {1, 2, 3} and $\text{R}=\{(\text{a, b}):|\text{a}^2-\text{b}^2|\leq5,\text{a, b}\in\text{A}\}$
For the elements of the given set A, we find that
$|1^2-1^2|\leq5,|2^2-2^2|\leq,5|3^2-3^2|\leq5,\\|1^2-2^2|\leq5,|2^2-1^2|\leq5,|2^2-3^2|\leq5,$ and $|3^2-2^2|\leq5$
$\Rightarrow\text{R}=\{(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)\}$

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