(a) plot the set {(x,y) ∈ r^2: fxy(x,y) > 0 in matlab

To plot the set {(x, y) ∈ R^2 : fxy(x, y) > 0} in MATLAB, you can start by defining a function fxy that represents your criteria. Then, you can create a grid of points in the x-y plane, evaluate fxy at those points, and finally plot the points that satisfy the condition fxy(x, y) > 0.

Here's an example code snippet to achieve this:

main.m
% Define the function fxy
fxy = @(x, y) x.^2 + y.^2 - 1; % Example function x^2 + y^2 - 1

% Create a grid of points in the x-y plane
[X, Y] = meshgrid(-10:0.1:10, -10:0.1:10);

% Evaluate fxy at the grid points
Z = fxy(X, Y);

% Plot points where fxy(x, y) > 0
figure;
contourf(X, Y, Z, [0 inf]);
colorbar;
title('Plot of {(x, y) ∈ R^2 : fxy(x, y) > 0}');
xlabel('x');
ylabel('y');
axis equal;
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In this example, we defined a simple function fxy as x^2 + y^2 - 1. You can replace this with your actual function. We then created a grid of points using meshgrid, evaluated fxy at those points, and plotted the contour plot using contourf with the condition fxy(x, y) > 0.

Make sure to adjust the function fxy and the range of points in the meshgrid based on your specific problem.