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 ?

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- Oct 5th 2013, 12:43 PMlamentofkingShow that if A and B are sets with A ⊆ B, then A ∪ B = B.
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 ? - Oct 5th 2013, 01:03 PMPlatoRe: Show that if A and B are sets with A ⊆ B, then A ∪ B = B.
- Oct 6th 2013, 01:45 PMlamentofkingRe: Show that if A and B are sets with A ⊆ B, then A ∪ B = B.
- Oct 6th 2013, 01:55 PMPlatoRe: Show that if A and B are sets with A ⊆ B, then A ∪ B = B.
- Oct 6th 2013, 04:48 PMHallsofIvyRe: Show that if A and B are sets with A ⊆ B, then A ∪ B = B.
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 .