Home
Class 12
MATHS
Let ""^(**):QxxQtoQ is defined by a^(**)...

Let `""^(**):QxxQtoQ` is defined by `a^(**)b=1+ab,AA a,b in Q`. Show that `""^(**)` is commutative, but not associative.

Text Solution

Verified by Experts

The correct Answer is:
`""^('**')` is not associative
Promotional Banner

Similar Questions

Explore conceptually related problems

Let ""^(**) be a binary operation on Q, defined by a^(**)b=(3ab)/(5) . Show that ""^(**) is commutative, if it exists.

Let A=NxxN and let ** be a binary operation on A defined by (a,b)**(c,d)=(a+c,b+d) . Show that ** is commutative and associative.

Consider a binary operation ""^(**) on N defined by a^(**)b=a^(3)+b^(3),a,b in N , Examine, if ""^(**) is commutative

Consider a binary operation ""^(**) on N defined by a^(**)b=a^(3)+b^(3),a,b in N , Examine, if ""^(**) is associative

Let ** be an operation defined on R by a**b=a+b+2ab . Show that ** is a binary operation on R. examine commutatively, associatively and existence of identity. Find the elements, if any, which have inverses.

Consider the ninary operation ""^(**) on N defined by a^(**)b="HCF" of a and b. Examine, if ""^(**) is commutative

Consider the binary operation ""^(**) on N defined by a^(**)b="LCM" of a and b. Examine, if ""^(**) is commutative

Is the binary operation ** defined by Q by a**b=(a+b)/2 for all a,b in Q commutative and associative?

Consider the binary operations ""^(**):RxxRtoR and o:RxxR defined by a^(**)b=|a-b| aob=a, AA a,b in R Examine, if o distributes over ""^(**) .