Show that if A and B are sets with A ⊆ B, then A ∪ B = B.
Is A ∪ B = B. because A ∪ B, Means A or B or Both ?
The rigorous way of showing that " " is to show that " " and that " ". And to show that " " start with "if and use the conditions on X and Y to conclude "therefore ".
So to show that, you must first show . And you do that by saying "if then either or (by definition of " " and then do it in two cases:
1) If we are done.
2) if then because , .
So that in either case, if then .
All that remains is to show that . To do that, if then by definition of .