Assignment #2, Question 3a.

Which of the 16 binary operations are commutative?

Recall the definition of commutative: f(x,y) = f(y,x).

We can say OR is commutative because if x=(0011) and y=(0101), then xORy=(0111) and yORx=(0111).

After working on the other 15 binary operations in a similar manner, I found the following list of binary operations which are commutative.

(0000)=y AND NOT(y)=y AND NOT(y)
(0001)=x AND y=y AND x
*(0011)=trivial
*(0101)=trivial
(0110)=x XOR y = y XOR x
(0111)=already shown
(1000)=NOT(x OR y)=NOT(y OR x)
(1001)=x IFF y=y IFF x
*(1010)=NOT(y)=NOT(y)
*(1100)=NOT(x)=NOT(x)
(1110)=NOT(x AND y)=NOT(y AND x)
(1111)=NOT(x) OR x

Not certain about the ones with *.