Final answer:
The relation R described is anti-symmetric, as it holds that for any x and y, if xRy and yRx, then x must equal y.
Step-by-step explanation:
The provided question describes a relation R where for any pair (x, y), the relation holds if dxe ≤ dye. The description that accurately describes relation R is anti-symmetric. The reason is that if dxe ≤ dye and dye ≤ dxe, we must have dxe = dye. So if x is related to y, and y is related to x, then x must equal y. This satisfies the condition of an anti-symmetric relation where for all x, y in the domain, if xRy and yRx, then x = y. This relation cannot be symmetric because if dxe < dye for some pair (x, y), it is not guaranteed that dye ≤ dxe and hence xRy does not always imply yRx. As for anti-reflexive, a relation R is anti-reflexive if no element is related to itself; however, in this case, it is clear that for any x, dxe ≤ dxe holds, so the relation is not anti-reflexive either. Finally, the relation is not symmetric as it does not hold that for all x and y, if xRy, then yRx.