Question:
According to the Principle of Inclusion-Exclusion, for two sets A and B, the formula for |A ∪ B| is:
According to the Principle of Inclusion-Exclusion, for two sets A and B, the formula for |A ∪ B| is:
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Add both sizes, then subtract the shared part once.
Updated On: Jul 2, 2026
- |A| × |B|
- |A| + |B|
- |A| + |B| − |A ∩ B|
- |A| ∩ |B|
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The Correct Option is C
Solution and Explanation
Step 1: When you add \(|A|\) and \(|B|\), every element in the overlap \(A \cap B\) is counted twice.
Step 2: To fix the double counting, subtract the size of the intersection once.
Step 3: This gives the inclusion-exclusion formula: \[ |A \cup B| = |A| + |B| - |A \cap B|. \]
Step 2: To fix the double counting, subtract the size of the intersection once.
Step 3: This gives the inclusion-exclusion formula: \[ |A \cup B| = |A| + |B| - |A \cap B|. \]
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