Determine which of these relations are transitive. the variables x, y, x', y' represent integers.

Answer: A. xâĽy if and only if xy is positive. B. xâĽy if and only if x+y is even. C. xâĽy if and only if xâ’y is a multiple of 10. D. xâĽy if and only if xâ’y is positive. E. xâĽy if and only if x+y is odd. A. xy is positive, so xy>0. So if x >=1, then (x, x) is satisfied. True B. If x+y is even, then x and y are both even or both odd. So odd (1,1) is even and even (2,2) is even. Therefore true C. x-y is a multiple of 10, but x-x is always 0, so its false. D. x-y is positve, but if x (1) and y (0) then (x, x) is 0, not positive, therefore false. E. x+y is odd therefore x is odd and y is even, or x is even and y is odd. But even + even, and odd + odd is always even. Therefore false.