If A and B are non-empty subsets of a set C, then A∪(A∩B) is equal to
- AA∩B
- BA∪B
- CA
- DB
Solution & Step-by-step Explanation
This problem can be solved using the fundamental Absorption Law in set theory.
Let's analyze the expression logically:
The intersection operation (A∩B) contains elements that are present in both set A and set B. This means (A∩B) is a subset of A ((A∩B)⊆A).
Taking the union of set A with one of its own subsets (A∩B) doesn't add any new elements outside of A. The elements of A absorb the subset completely:
A∪(A∩B)=A
Let's analyze the expression logically:
The intersection operation (A∩B) contains elements that are present in both set A and set B. This means (A∩B) is a subset of A ((A∩B)⊆A).
Taking the union of set A with one of its own subsets (A∩B) doesn't add any new elements outside of A. The elements of A absorb the subset completely:
A∪(A∩B)=A