If universal Set u={1, 2 ,3..15} A = {1, 5, 8, 10,14,15} and B={2,4,6,8,10,12,} Verify De Morgan's Laws

De Morgan's Laws state:

1. \((A \cup B)' = A' \cap B'\)
2. \((A \cap B)' = A' \cup B'\)

Where:
- \(A'\) is the complement of \(A\), i.e., all elements in the universal set \(U\) that are not in \(A\).
- \(B'\) is the complement of \(B\), i.e., all elements in the universal set \(U\) that are not in \(B\).
- \(A \cup B\) is the union of sets \(A\) and \(B\).
- \(A \cap B\) is the intersection of sets \(A\) and \(B\).

Let's verify each law.

### Given:
- Universal set \(U = \{1, 2, 3, \ldots, 15\}\)
- \(A = \{1, 5, 8, 10, 14, 

Understand and verify De Morgan's Laws with sets A and B within the context of the universal set U. Learn how to apply set theory principles to prove these fundamental laws. Suitable for advanced high school students and beyond.

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