Please it is very urgent. Is abstract mathematics (Ring property I think). Kindly provide correct solution, I will thumb up

this is very clear enough. please enlarge it

is an Econometrics term

3. Suppose that X = {w,,y,). Consider the choice structure denoted by (98,C(-)), such that B = {{w,y,z}, {r,y}, {y, z},{x,z},{r,y,z}} and: C({w.y =)) = {w} C({x,y}) = {u} C({y,z)) = {v} C({.,2)) = {2} What choice rules for C({6,7,2}) satisfy WARP, if any? Prove your answer. II Consumer Choice 4. Suppose that the Walrasian demand function x(p.w) satisfies WARP. Prove that rap, aw) = (p, w) for any a > 0. Walras' law WARP then it follows that, if the price of commodity & decreases, its compensated demand 1() must necessarily increase. Suppose X R. What does this result imply for the compensated cross-price effect? Prove your answer. 2 3. Suppose that X = {w,,y,). Consider the choice structure denoted by (98,C(-)), such that B = {{w,y,z}, {r,y}, {y, z},{x,z},{r,y,z}} and: C({w.y =)) = {w} C({x,y}) = {u} C({y,z)) = {v} C({.,2)) = {2} What choice rules for C({6,7,2}) satisfy WARP, if any? Prove your answer. II Consumer Choice 4. Suppose that the Walrasian demand function x(p.w) satisfies WARP. Prove that rap, aw) = (p, w) for any a > 0. Walras' law WARP then it follows that, if the price of commodity & decreases, its compensated demand 1() must necessarily increase. Suppose X R. What does this result imply for the compensated cross-price effect? Prove your answer. 2