Show that * on `Z^(+)` defined by a*b=|a-b| is not binary operation

Show that * On Z^(+) defined by a*b = |a-b| is a binary operation or not.

Show that * On R defined by a*b = a +4 b^(2) is a binary operation or not.

Is * defined by a * b=(a+b)/2 is binary operation on Z.

Is * defined by a^(*)b=(a+b)/(2) is binary operation on Z.

Which of the following is true? * defined by a*b=(a+b)/2 is a binary operation on Z (b) * defined by a*b=(a+b)/2 is a binary operation on Q (c) all binary commutative operations are associative (d) subtraction is a binary operation on N

Which of the following is true? * defined by (a) a*b=(a+b)/2 is a binary operation on Z (b) * defined by a*b=(a+b)/2 is a binary operation on Q (c) all binary commutative operations are associative (d) subtraction is a binary operation on N

The operation ** defined by a ** b =(ab)/7 is not a binary operation on

Show that the operation ** defined on RR-{0} by a**b=|ab| is a binary operation. Show also that ** is commutative and associative.

Prove that the operation ** on ZZ defined by a**b=a|b| for all a,binZZ is a binary operation