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gavbacardi
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1. {(x,y)[itex]\in[/itex] R^2 such that 2x+y<=2, x-y>4} Determine whether this subset of R^2 is open, closed or neither open nor closed.
2. I think this is an open subset but not sure how to prove it. I have rearranged the equations to give x>2, y<=-2x+1, y< x-1. I think it is open because x can get closer and closer to 2 but never equal it and y can get closer and closer to x-1 but never equal it. I'm not sure how prove this mathematically though?
Any help or hints would be great!
2. I think this is an open subset but not sure how to prove it. I have rearranged the equations to give x>2, y<=-2x+1, y< x-1. I think it is open because x can get closer and closer to 2 but never equal it and y can get closer and closer to x-1 but never equal it. I'm not sure how prove this mathematically though?
Any help or hints would be great!