Which of these is TRUE or FALSE?

1. The binary relation>on the set of real numbers is reflexive.
2. The binary relation = on the set of real numbers is complete.
3. The lexicographic ordering onR₊²is transitive.
4. The preference relation represented by the utility functionu(x1, x2) :=x1x2for all nonnegative (x1 , x2) is continuous.
5. Given utility functionu(x1, x2) := (x11)²+ (x21)² for all nonnegative (x1, x2), any optimum of the consumer's decision problem belongs to the budget line.
6. The binary relationdefined by (x1,x2)(x1,x2) 1 x1+ x2 (x1+x2) 1is transitive on R₊².
7. The binary relation defined by the above formula (6) is reflexive on R₊².
8. The binary relation defined by the above formula (6) is complete on R₊²
9. The lexicographic ordering on the set of nonnegative integer pairs (i.e., pairs (m, n) such thatmandnare elements of the set{0,1,2,3,}) can be represented by a utility function.