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    OlympiadMediumCombinatorics7–9

    Inclusion-Exclusion

    Inclusão-Exclusão

    How many integers from 1 to 100 are divisible by 2 or 3?

    Use ∣A∪B∣=∣A∣+∣B∣−∣A∩B∣|A \cup B| = |A| + |B| - |A \cap B|.

    Solution

    Step 1 of 4

    1. 1.∣A∣=⌊1002⌋=50|A| = \lfloor \tfrac{100}{2} \rfloor = 50 (divisible by 2)