written 2.1 years ago by | • modified 2.1 years ago |
Consider a set of integers from 1 to 250.
(A) Find how many ways of these numbers are divisible by 3 or 5 or 7? Also
(B) Indicate how many are divisible are divisible by 3 or 5 but not by7?
written 2.1 years ago by | • modified 2.1 years ago |
Consider a set of integers from 1 to 250.
(A) Find how many ways of these numbers are divisible by 3 or 5 or 7? Also
(B) Indicate how many are divisible are divisible by 3 or 5 but not by7?
written 2.1 years ago by | • modified 2.1 years ago |
Solution:
$\rightarrow \quad x=250$
$\quad|A|=\left|\frac{250}{3}\right|=83$
$\quad|B|=\left|\frac{250}{5}\right|=50$
$\quad|C|=\left|\frac{250}{7}\right|=35$
$ \quad|A \cap B|=\left|\frac{250}{3 \times 5}\right|=16$
$ \quad|B \cap C|=\left|\frac{250}{5 \times 7}\right|=7$
$ \quad|A \cap c|=\left|\frac{250}{3 \times 7}\right|=11$
$\quad|A \cap B \cap C|=\left|\frac{250}{3 \times 5 \times 7}\right|=2$
(A) Find how many ways of these numbers are divisible by 3 or 5 or 7: …