Question

given sets A and B prove A<=AUB

Answer 1

you need to define what A and B are..!

Answer 2

yes exactly..but you need to specify the elements of set
for example if A and B are mutually exclusive sets then
A∪B=A+B
and in that case A<=A+B if B has no elements or empty set
but if they are not mutually exclusive and have some common elements then union of two sets largely depends on no of elements they have in common so you have to be precise about the no of elements in the sets