duck wrote

Hi.. :)

Given, A+B = B

⇒ A+B ⊆ B and B ⊆ A+B

⇒ (A-B) ∪ (B-A) ⊆ B [From A+B ⊆ B]

⇒ **(A-B) ⊆ B**

⇒ A ⊆ B

Hence, proved!

focussing at the bold part of your text:

**A-B** means all those elements of

**A** which are

**not present** in B. ie if we remove all the elements of

**A** which are in

**B** and if still this set is a subset of B

**implies **it still contains some elements (at least 0 elements) of

**B**. But this contradicts our definition of

**A-B** since

**A-B** cant have any element which is present in

**B**. So

**A** has to be an empty set...

what am I missing?

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"You don't have to believe in God, but you should believe in The Book." -Paul Erdős