Consider the binary operations `** \: R\ xx\ R -> R ` and `o\ : R\ xx\ R -> R` defined as a `**\ b=|a-b|` and `a` `o` `b=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. Further, show that * is distributive over o . Dose o distribute over * ? Justify your answer.

Consider the binary operations *:" "RxxR ->R and o:" "R" "xx" "R->R defined as a*b|a-b| and a" "o" "b" "=" "a , AA""""a ," "b in R . Show that * is commutative but not associative, o is associative but not commutative.

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

Let * be a binary operation on N defined by a*b = a^(b) for all a,b in N show that * is neither commutative nor associative

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

Show that *:R xx R rarr R given by a*b=a+2b is not associative.

Consider a binary operation. on N defined a ** b = a^3 + b^3. Choose the correct answer. (A) Is ** both associative and commutative? (B) Is ** commutative but not associative? (C) Is ** associative but not commutative? (D) Is ** neither commutative nor associative?

On Z an operation * is defined by a*b=a^(2)+b^(2) for all a,b in Z .The operation* on Z is commutative and associative associative but not commutative (c) not associative (d) not a binary operation