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Question
Let A = {1, 2, 3} and\[R = \left\{ \left( a, b \right) : \left| a^2 - b^2 \right| \leq 5, a, b \in A \right\}\].Then write R as set of ordered pairs.
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Solution
Given:
A = {1, 2, 3}
\[R = \left\{ \left( a, b \right) : \left| a^2 - b^2 \right| \leq 5, a, b \in A \right\}\]
We know that
\[\left| 1^2 - 1^2 \right| \leq 5, \]
\[\left| 2^2 - 2^2 \right| \leq 5, \]
\[\left| 3^2 - 3^2 \right| \leq 5, \]
\[\left| 1^2 - 2^2 \right| \leq 5, \]
\[\left| 2^2 - 1^2 \right| \leq 5, \]
\[\left| 2^2 - 3^2 \right| \leq 5, \]
\[\left| 3^2 - 2^2 \right| \leq 5\]
Thus, R ={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}
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