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If R2={(x,y)| x and y are integers and ...

If `R_2={(x,y)| x and y` are integers and `x^2 +y^2=64`} is a relation. Then find `R_2`.

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To find the relation \( R_2 = \{(x, y) | x \text{ and } y \text{ are integers and } x^2 + y^2 = 64\} \), we will follow these steps: ### Step 1: Understand the equation The equation \( x^2 + y^2 = 64 \) represents a circle with a radius of 8 centered at the origin in the coordinate plane. We are looking for integer solutions (lattice points) on this circle. ### Step 2: Determine possible values for \( x \) Since \( x^2 \) must be less than or equal to 64, the possible integer values for \( x \) range from \(-8\) to \(8\): \[ ...
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