Questions: Fill in the blank below. The of sets A and B, written A ∪ B, is the set of elements that are members of either A or B (or both). Using set-builder notation, A ∪ B=x: x is a member of A or x is a member of B. exclusion inclusion complement intersection union difference

Fill in the blank below. The of sets A and B, written A ∪ B, is the set of elements that are members of either A or B (or both). Using set-builder notation, A ∪ B=x: x is a member of A or x is a member of B. exclusion inclusion complement intersection union difference
Transcript text: Fill in the blank below. The $\qquad$ of sets $A$ and $B$, written $A \cup B$, is the set of elements that are members of either $A$ or $B$ (or both). Using set-builder notation, $A \cup B=\{x: x$ is a member of $A$ or $x$ is a member of $B\}$. exclusion inclusion complement intersection union difference
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Solution

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Solution Steps

Solution Approach

The question is asking for the term that describes the operation of combining all elements from two sets, which is known as the "union" of sets. The union of sets \(A\) and \(B\), denoted as \(A \cup B\), includes all elements that are in either set \(A\) or set \(B\) or in both.

Step 1: Define Sets \(A\) and \(B\)

We start by defining two sets, \(A\) and \(B\). In this case, set \(A\) is \(\{1, 2, 3\}\) and set \(B\) is \(\{3, 4, 5\}\).

Step 2: Calculate the Union of Sets

The union of two sets \(A\) and \(B\), denoted as \(A \cup B\), is the set of elements that are members of either \(A\) or \(B\) or both. Mathematically, this can be expressed as: \[ A \cup B = \{x : x \in A \text{ or } x \in B\} \]

Step 3: Determine the Elements in the Union

By examining the elements in sets \(A\) and \(B\), we find that the union \(A \cup B\) includes all unique elements from both sets. Therefore, the union is: \[ A \cup B = \{1, 2, 3, 4, 5\} \]

Final Answer

The union of sets \(A\) and \(B\) is \(\boxed{\{1, 2, 3, 4, 5\}}\).

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