operator A @ and operator # @ A B C D A A B A B B B B B B C A B C D D B B D D #

Question

operator A @ and operator # @ A B C D A   A  B  A B B   B B   B B C   A B   C D D   B   B D   D # A B C D A   A  A  C C B   A B   C D C   C  C   C C D   C   D  C  D Q: Which Axiom hold(s) and which do(es) hold? Axiom 1: Closure Axiom 2: Identity Axiom 3: Commutativity Axiom 5: Complement Thank you very much operator A @ and operator # @ A B C D A   A  B  A B B   B B   B B C   A B   C D D   B   B D   D # A B C D A   A  A  C C B   A B   C D C   C  C   C C D   C   D  C  D Q: Which Axiom hold(s) and which do(es) hold? Axiom 1: Closure Axiom 2: Identity Axiom 3: Commutativity Axiom 5: Complement Thank you very much # A B C D A   A  A  C C B   A B   C D C   C  C   C C D   C   D  C  D Q: Which Axiom hold(s) and which do(es) hold? Axiom 1: Closure Axiom 2: Identity Axiom 3: Commutativity Axiom 5: Complement Thank you very much

Explanation / Answer

closure property holds for both @ and # since the result setconsists of only ( A,B,C,D) Identity for @ is C # is B commutativity holds for @ and # since the table is symmetricalong diagonals not sure about complement..

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