Sets Operations

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If A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}, then find the number of elements in (A ∪ B) - (A ∩ B).

RankGuru · Accepted Answer

1. **Determine Union ($A \cup B$)**: Combine all unique elements from both sets.
   - $A \cup B = \{1, 2, 3, 4, 5, 6, 7\}$. Total elements = 7.
2. **Determine Intersection ($A \cap B$)**: Elements common to both sets.
   - $A \cap B = \{3, 4, 5\}$. Total elements = 3.
3. **Set Difference**: Remove elements of intersection from the union.
   - $(A \cup B) - (A \cap B) = \{1, 2, 6, 7\}$.
4. **Count**: The result set has **4** elements. This operation is known as the **Symmetric Difference** ($A \Delta B$).

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