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The Cartesian Plane over the field F where "+" and "." are defined by (mod 2). (a) Fill the following table of “+” and “.”: + 0 1 . 0 1 0 1 Consider Z2 = {0,1}, 0 1 Remark From the above two tables, one can easily see that Z₂ is a field. (b) The Cartesian plane over the field F is the set Fx F = {(x, y) x,y≤F} Find all points in the Cartesian plane over Z₂. (c) A line in the Cartesian plane over F is a subset defined by a linear equation {(x, y) = F x F ax+by+c= 0, a, b, c = F} Find all lines the in the Cartesian plane over Z₂.

The Cartesian Plane over the field F where "+" and "." are defined by (mod 2). (a) Fill the following table of “+” and “.”: + 0 1 . 0 1 0 1 Consider Z2 = {0,1}, 0 1 Remark From the above two tables, one can easily see that Z₂ is a field. (b) The Cartesian plane over the field F is the set Fx F = {(x, y) x,y≤F} Find all points in the Cartesian plane over Z₂. (c) A line in the Cartesian plane over F is a subset defined by a linear equation {(x, y) = F x F ax+by+c= 0, a, b, c = F} Find all lines the in the Cartesian plane over Z₂.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4. The Cartesian Plane over the field F where "+" and "." are defined by (mod 2). (a) Fill the following table of "+" and ".": + 0 1 0 1 0 1 Consider Z₂ = {0, 1}, 0 1 Remark From the above two tables, one can easily see that Z2 is a field. (b) The Cartesian plane over the field F is the set Fx F = {(x, y)| x,y≤F} Find all points in the Cartesian plane over Z₂. (c) A line in the Cartesian plane over F is a subset defined by a linear equation {(x, y) = F x F ax+by+c= 0, a, b, c = F} Find all lines the in the Cartesian plane over Z₂.
Transcribed Image Text:4. The Cartesian Plane over the field F where "+" and "." are defined by (mod 2). (a) Fill the following table of "+" and ".": + 0 1 0 1 0 1 Consider Z₂ = {0, 1}, 0 1 Remark From the above two tables, one can easily see that Z2 is a field. (b) The Cartesian plane over the field F is the set Fx F = {(x, y)| x,y≤F} Find all points in the Cartesian plane over Z₂. (c) A line in the Cartesian plane over F is a subset defined by a linear equation {(x, y) = F x F ax+by+c= 0, a, b, c = F} Find all lines the in the Cartesian plane over Z₂.
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