A ∪ ∅ = A. In set theory, the union of any set A with the empty set (∅) is always the set A itself.
Here's a breakdown:
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Union (∪): The union of two sets combines all the elements from both sets into a single set. Any element present in either set is included in the union.
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Empty Set (∅): The empty set is a set that contains no elements. It is also known as the null set.
Therefore, when you take the union of set A with the empty set, you are essentially combining the elements of A with nothing. Since the empty set has no elements to contribute, the resulting set contains only the elements of A.
Example:
Let A = {1, 2, 3}
Then A ∪ ∅ = {1, 2, 3} ∪ {} = {1, 2, 3} = A
This principle is a fundamental identity law in set theory.
