If A is a non empty set, prove that the operation union on P(A) is a binary operation.

Show that the operation * defined on Q-{1} by a**b=a+b-ab is abinary operation. Is * commutative and associative? What is the identity element wrt *? Which elements possess inverses?

Give an example to show that suntraction is not a binary operation on the set of natural numbers.

Does the operation * defined below on the given set represent a binary operation? : a**b=a+4b^2 on R

Does the operation * defined below on the given set represent a binary operation? : a**b=a-b on Z^+

Does the operation * defined below on the given set represent a binary operation? : a**b=ab on Z^+

Does the operation * defined below on the given set represent a binary operation? : a**b=(a+b)/2 on N

For any two sets A and B, prove that P(A nn B)=P(A) nn P(B)

Is * defined on the set A={1,2,3,4,5} by a**b=L.C.M. of a,b in A , a binary operation?

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.