For any two sets `A\ a n d\ B ,` prove that `AnnB=phi=>AsubeB^(prime)dot`

Explanation

To prove that if \( A \cap B = \phi \) (the intersection of sets A and B is the empty set), then \( A \subseteq B' \) (A is a subset of the complement of B), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**: We are given that \( A \cap B = \phi \). This means that there are no elements that are common between sets A and B.

2. **Take an Arbitrary Element from A**: Let \( x \) be an arbitrary element of set A. Therefore, we can say \( x \in A \).

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