Question

suppose that a and b are sets, defined as follows. find the intersection and union of a and b. enter the elements of the sets in increasing order, separated by commas. if a set is the empty set, just enter dne inside the box given.
a = {1, 2, 3, 4, 6, 7, 10} and b = {2, 4, 5, 6, 8, 10}
a ∩ b =
a ∪ b =

Explanation:

Step1: Find the intersection (elements common to both sets)

The intersection of two sets \( A \) and \( B \), denoted \( A \cap B \), consists of elements that are in both \( A \) and \( B \).
Set \( A = \{1, 2, 3, 4, 5, 6, 10\} \) and set \( B = \{2, 4, 5, 6, 8, 10\} \).
The common elements are \( 2, 4, 5, 6, 10 \). So \( A \cap B=\{2, 4, 5, 6, 10\} \).

Step2: Find the union (elements in either set)

The union of two sets \( A \) and \( B \), denoted \( A \cup B \), consists of elements that are in \( A \) or in \( B \) (or in both).
Combining the elements of \( A \) and \( B \) and removing duplicates:
From \( A \): \( 1, 2, 3, 4, 5, 6, 10 \)
From \( B \): \( 2, 4, 5, 6, 8, 10 \)
Combined and sorted: \( 1, 2, 3, 4, 5, 6, 8, 10 \). So \( A \cup B = \{1, 2, 3, 4, 5, 6, 8, 10\} \).

Answer:

\( A \cap B = \{2, 4, 5, 6, 10\} \)
\( A \cup B = \{1, 2, 3, 4, 5, 6, 8, 10\} \)