Assignment #2 Q 4 & 5

Q. How do things grow/change if you were working in trinary? That is assumed that there are three possible inputs {0,1,2}, how many possible binary operations are there?

Since there are three possible inputs {0, 1, 2} . Therefore, 3^9 = 19 683.
x 0 0 0 1 1 1 2 2 2
y 0 1 2 0 1 2 0 1 2

In Binary case , for two choices and four ways to arrange them; hence, there are 2^4=16 operations. In this case, we have three operations, and nine ways to arrange them; therefore, we have 3^9 operations.

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Problem # 5

How many binary operations are necessary so that compositions of these binary operations can be used to express every possible two argument function on ternary operations?

Solution:
Since the operations IMPL, OR, AND, and NOT can generate all 16 binary functions, these same four can generate every possible two argument function on trinary operations.So the function: NOT, OR, AND, and IMPL here are only 4 binary operations necessary so that compositions of these binary operations can be used to express every possible two argumen.