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5 17%) Consider a preference relation dened below: For any two bundles (x1, x2) and (x'l, 95/2), $1,:r2) is preferred to (x'1,:t'2)denoted (x1, x2) > (x'l, x'Z)if and only if z1+x2 2 z'1+x'2+3 e g., (3,4) > (1,3), but not (3,3) > (1,3)); the two bundles are indifferent, denoted (951,222) ~ sic/1&5), if and only if neither 9:1 : 9:2 2 w'l : 9H2 : 3 nor m'l : z'2 2 x1 : x2 : 3 is true. Denote W ( ( ( t for \"> or ~\". a. For each of the following statements, write \"T\" if it is true, and otherwise \"F\": i. (10,0) > (6,8). .@n~ma -@:@ ._.. i ._.. ii iv. N is reexive v. t is complete vi. > is transitive vii. t is transitive. viii. There exists a. utility function for i when there are at most countably many alter- natives. b. Fill in the blanks: i. (3,1) > (1,0) is ________________ (true, false). Thus, (3, 1) ~ (1,0) is ________________ (true, false) and (1,0) ~ (3, 1) is ,,,,,,,,,,,,,,,, (true, false). Thus, ~ is ,,,,,,,,,,,,,,,, (complete, not complete, not reexive). ii. Suppose that $1 + 122 = xi + 92'? + 3. Then ($1,902) ,,,,,,,,,,,,,,,, (5 ~, is not z, is not ~) (w'1,w'2). For any E > 0, $1 + $2 E 2 95/1 + x'z +3 is ________________ (true, false, undetermined) and hence ($1 6, $2) > (ac/1,955) is ________________ (true, false, undetermined). Thus, > is ,,,,,,,,,,,,,,,, (continuous, not continuous). If the set of alternatives is 1R1, there ________________ (exists, does not exist) a utility function for t