Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 5 Marks

Year: Dec 2013

Let A denotes numbers divisible by 2.

B denotes numbers divisible by 3. and C denotes numbers divisible by 7.

$$|A| =\bigg[\dfrac{1000}{2}\bigg]=500 \\ |B| =\bigg[\big[\dfrac{1000}{3}\big]\bigg]=333 \\ |C| =\bigg[\big[\dfrac{1000}{7}\big]\bigg]=143$$

$$|AՈB| =\bigg[\dfrac{1000}{2 \times3}\bigg]=167 \\ |AՈC| =\bigg[\big[\dfrac{1000}{2 \times7}\big]\bigg]=71 \\ |BՈC| =\bigg[\big[\dfrac{1000}{3 \times7}\big]\bigg]=48 \\ |AՈBՈC| =\bigg[\big[\dfrac{1000}{2\times3\times7}\big]big]=24$$

$|A U B U C|$ $=|A| + |B| + |C| + [|A Ո B| + |A Ո C| + |B Ո C| + |A Ո B Ո C|] \\ =500 + 333 + 143 + 167 + 71 + 48 + 24 \\ =1286$

This shows 1286 numbers are divisible by 2, 3 0r 5. Hence numbers which are divisible by 3 only but not by 2 nor by 5.

$=|B| - |A Ո C| \\ =333-71 \\ =262$