5) Consider the following sets, S, together with the defined binary operation. In each case, determine...

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5) Consider the following sets, S, together with the defined binary operation. In each case, determine if the set is closed under the given operation, if the operation is associative and if the operation is commutative: (i) S=Z a*b= 2ab + 7 (ii) S=Q a*b = /ab = a'b (iii) S = R a*b (iv) S=Z a*b= 2ab + 7b (v) S= R+ a*b= /ab 6) Define the binary operation, multiplication modulo 3 in much the same way as we did addition modulo 3. That is, perform ordinary multiplication and then reduce the result modulo 3. Let S = {0, 1, 2}. Create two tables, one giving the operation addition modulo 3 on S and the other giving the operation multiplication modulo 3 on S. Show that these two binary structures cannot possibly be isomorphic to one another. 5) Consider the following sets, S, together with the defined binary operation. In each case, determine if the set is closed under the given operation, if the operation is associative and if the operation is commutative: (i) S=Z a*b= 2ab + 7 (ii) S=Q a*b = /ab = a'b (iii) S = R a*b (iv) S=Z a*b= 2ab + 7b (v) S= R+ a*b= /ab 6) Define the binary operation, multiplication modulo 3 in much the same way as we did addition modulo 3. That is, perform ordinary multiplication and then reduce the result modulo 3. Let S = {0, 1, 2}. Create two tables, one giving the operation addition modulo 3 on S and the other giving the operation multiplication modulo 3 on S. Show that these two binary structures cannot possibly be isomorphic to one another.

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