Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 6 Marks

Year: May 2016

Let A denotes numbers divisible by 2

B denotes numbers divisible by 3.

and C denotes numbers divisible by 5.

$|A| =\bigg[\dfrac{60}{2}\bigg]=30$

$|B| =\bigg[\big[\dfrac{60}{3}\big]\bigg]=20$

$|C| =\bigg[\big[\dfrac{60}{5}\big]\bigg]=12$

$|AՈB| =\bigg[\dfrac{60}{2 \times 3}\bigg]=10$

$|AՈC| =\bigg[\big[\dfrac{60}{2 \times 5}\big]\bigg]=6$

$|BՈC| =\bigg[\big[\dfrac{60}{3 \times 5}\big]\bigg]=4$

$|AՈBՈC| =\bigg[\big[\dfrac{60}{2 \times 3 \times 5}\big]\bigg]=2$

Now the numbers divisible by 2 but not by 3 and nor by 5.

=|A|-|B ̅ՈC ̅|

=|A|-[|B|+|C|-|B Ո C|]

=30-[20+12-4]

=30-28

=2

This shows 2 numbers are divisible by 2 but not by 3 and nor by 5.