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In this question we will refer to a system that includes the four axioms of the group; Its basic concept is "binary action". It is permissible to use the fact that the addition and multiplication modulo operations are collective, without proving it. A. Prove that the system is without contradiction. B. Proved that axiom 2 does not derive from the other axioms. c. Proved that axiom 4 does not derive from the other axioms. D. We will add Axiom 5: there are exactly 4 limbs. Prove that the group {1,3,5,7} with respect to the multiplication operation Modulo 8 is a model for the system (1,2,3,4,5). e. Prove that the system (1,2,3,4,5) is not categorical.

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