Final Answer:
The intersection of set A with the union of sets B and C (A∩(B∪C)) is {1,2}.
Step-by-step explanation:
In set theory, the intersection of two sets is the collection of elements that are common to both sets. The union of two sets, on the other hand, includes all unique elements from both sets. In this case, set A={1,2} intersects with the union of sets B={2,4,6,8,10,12,14} and C={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}. The union of B and C is the set containing all distinct elements from both B and C, resulting in B∪C={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}. The intersection of A with B∪C gives us the common elements between A and the union of B and C, which are {1,2}.
This result is obtained by identifying the elements that are present in both A and the union of B and C. In this case, 1 and 2 are the only common elements. No other elements from A intersect with the union of B and C, leading to the final answer of A∩(B∪C)={1,2}.
The reason for this outcome is the nature of set intersection, which focuses on the common elements between sets. The set A∩(B∪C) specifically looks at the elements that are shared between A and the union of B and C. In this scenario, only 1 and 2 are common to both A and B∪C, resulting in the final answer of {1,2}.