1. Determine if the following sets are bounded, open, closed, compact, convex: a) {(x, y) € R2 : (x< 1, \y\ <2}; b) {(x,

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1 Determine If The Following Sets Are Bounded Open Closed Compact Convex A X Y R2 X 1 Y 2 B X 1 (39.49 KiB) Viewed 25 times

Please I need answers to these problems
with explanations.
1. Determine if the following sets are bounded, open, closed, compact, convex: a) {(x, y) € R2 : (x< 1, \y\ <2}; b) {(x, y, z) € R3 : 2x + y - 32 5 7}; c) {(x, y, z) € R3 : \x+y+z1 <1}; d) {(x,y) € R2 : x2 +9y? > 1}; e) {(x, y) € R2 : 3 + 4x + x² + y2 <0}; f) {(x, y) € R2 : xy > 1}; g) {(x, y) € R2 : x + y2 <1}; 3 h) {(x, y, z) € R3 : x > \yl}; i) {(x,y,z) e R$ : 45x2 + y2 + x2 < 9}; j) {(x, y, z) € R3 : x2 + y2 + 2 > 1, x2 + y2 + x2 <4}. ху . 2