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. Further, show that `AAa

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.

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*: RxR rarr and o:RxR rarr 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.

The binary operation *:R xx R rarr R is defined as a*b=2a+b* Find (2*3)*4

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?

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.

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