Data:
A = integers divisible by 3
B = integers divisible by 5
C = integers divisible by 7
Total integers = 500
Formula:
A ∪ B ∪ C = A + B + C – (A ꓵ B) – (A ꓵ C) – (B ꓵ C) + (A ꓵ B ꓵ C)
Calculation:
A = \(\frac{{500}}{3}\) , B = \(\frac{{500}}{5}\), C = \(\frac{{500}}{7}\), A ꓵ B = \(\frac{{500}}{{3 \times 5}}\)
A ꓵ C = \(\frac{{500}}{{3 \times 7}}\),
B ꓵ C = \(\frac{{500}}{{5 \times 7}}\) and A ꓵ B ꓵ C = \(\frac{{500}}{{3 \times 5 \times \;7}}\)
A ∪ B ∪ C = \(\frac{{500}}{3} + \frac{{500}}{5} + \frac{{500}}{7} - \frac{{500}}{{3 \times 5}} - \frac{{500}}{{3 \times 7}} - \frac{{500}}{{5 \times 7}} + \frac{{500}}{{3 \times 5 \times \;7}}\)
= 271
Number of integers divisible by 3 or 5 or 7 = 271
