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.

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?

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)/2 on N

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^+

Is the binary operation ** defined on Z (set of integers) by the rule a**b=a-b+ab for all a, bin Z commutative ?

Given the sets A = {1,2, 3, 4, 5} and B = {1, 3, 5}, write R as a set of ordered pairs, if the relation R from A to B is defined by ‘x isless than y’. State the domain and the range of the relation

Define a relation in the set A={1,2,3,4} which is transitive but not symmetric.