FOR ANY TWO SETS `Aa n dB` , show that the following statements are equivalent: `AsubB` (ii) `A-B=varphi` (iii) `AuuB=B` (iv) `AnnB=Adot`

Explanation

To show that the following statements are equivalent for any two sets \( A \) and \( B \):

1. \( A \subseteq B \)
2. \( A - B = \varnothing \)
3. \( A \cup B = B \)
4. \( A \cap B = A \)

We will prove that each statement implies the next, forming a chain of equivalences.
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