ASSIGNMENT # 2 Q 3(a)

Q3 (a) which of the 16 binary operations are commutative?

By definition a function is said to be a commutative function if f(x, y) = f(y, x).
So commutative functions are:

[0,0,0,0] =x XOR x

[0,0,0,1]=x XOR ((x IMPL y) XOR ((x XOR x) IMPL(x XOR y)))

[0,0,1,1]=x

[0,1,0,1]=y

[0,1,1,0]=x XOR y

[0,1,1,1]=y XOR ((x IMPL y) XOR ((x XOR x) IMPL(x XOR y)))

[1,0,0,0]=x XOR(y IMPL x)

[1,0,0,1]=(x XOR y) IMPL(x XOR x)

[1,0,1,0]=y IMPL(x XOR x)

[1,1,0,0]=x IMPL(x XOR x)

[1,1,1,0]=x IMPL(x XOR y)

[1,1,1,1]=(x XOR x) IMPL (x XOR y)