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Question regarding lattices [closed]

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In Question 1 of the current exercise why is R5 a lattice and R3 not? At first I thought I had understood the solution but the more I think about this the more I get confused by it. Maybe I do not understand the definition of greates lower and lowest upper bound correctly.

closed with the note: Question answered
in * TF "Emb. Sys. and Rob." by (800 points)
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Read the following hints one by one. Think whether you can figure out the answer. If you can't continue with the next one:

  1. Look at R4 and R6. Do you see how R4 differs from R3, and how R6 differs from R5?
  2. We agree that R5 is a lattice. Hence, there's a a supremum and an infimum for every pair of elements. What's the infimum of {3, 7} in R5? Is there an infimum of {3, 7} in R3?
  3. Maybe you are confused by the natural numbers and orderings on these. Try to abstract from that. Imagine that the elements in R3 are just some elements that have nothing in common with any set or relation you know.
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