Question: Let = ^+ ^. (^ + are the positive integers, ^ are negative integers) Define a relation R on as follows: For all (, )

Let = ^+ ^. (^ + are the positive integers, ^ are negative integers) Define a relation R on as follows: For all (, ) and (, ) in A, (, )(, ) if + . Prove that is not reflexive. (Rather than give a counterexample, show that no element could possibly be related to itself.) Give a counterexample and show that R is not symmetric. Prove that R is antisymmetric. (Hint: This is a tricky one.)

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