Consider the binary operations `** \: R\ xx\ R -> R ` and `o\ : R\ xx\ R -> R` defined as a `**\ b=|a-b|` and `aob=a` for all `a,\ b\ in R`. Show that `**` is commutative but not associative, `o` is associative but not commutative.

Consider the binary operations *: RxxR->R and o: RxxR->R defined as a*b=|a-b| and aob=a for all a ,\ b in Rdot Show that * is commutative but not associative, o is associative but not commutative.

Consider the binary operation * : R xx R rarr R and o : R xx R rarr R defined as a * b = |a-b| and a o b = a, AA a, b in R . Is o distributive over * ? Justify your answer.

Let * be a binary operation on Z defined by a*b= a+b-4 for all a ,\ b in Zdot Show that * is both commutative and associative.

Consider the binary operations ""^('ast') and 'o' on R defined as a^(ast)b=abs(a-b) and aob=a , for all a, b in R . Show that a^(ast)(boc)=(a^(ast)b)oc for all a, b, c in R.

Show that * : R xx R to R defined by: a * b =a-5b is not abelian.

Prove that **: R xx R to R defined as a ** b =a+2ab is not associative

If * is a binary operation in N defined as a*b =a^(3)+b^(3) , then which of the following is true : (i) * is associative as well as commutative. (ii) * is commutative but not associative (iii) * is associative but not commutative (iv) * is neither associative not commutative.

The binary operation * defined on N by a*b= a+b+a b for all a ,\ b in N is (a) commutative only (b) associative only (c) commutative and associative both (d) none of these

Prove that **: R xx R to R defined as a ** b =a+2ab is not commutative .

A binary operation * on Z defined by a*b= 3a+b for all a ,\ b in Z , is (a) commutative (b) associative (c) not commutative (d) commutative and associative