.\

1a**b=\\\\sqrt(|ab|)

, on the set

Q

.\

2a^(**)b=alnb

, on the set

{xinR:x>0}

.\

3a**b

is a root of the equation

x^(2)-a^(2)b^(2)=0

, on the set

R

.\ 4 Subtraction, on the set

z

.\ 5 Subtraction, on the set

{ninz:>=0}

.\

6a**b=|a-b

|, on the set

{ninz:>=0}

.

is not an integer.) Thus, z is not closed under *. 1ab=ab, on the set Q. 2ab=alnb, on the set {xR:x>0}. 3ab is a root of the equation x2a2b2=0, on the set R. 4 Subtraction, on the set z. 5 Subtraction, on the set {nz:0}. 6ab=ab, on the set {nz:0}