Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 8 Marks

Year: Dec 2014

Let A denotes numbers divisible by 2

B denotes numbers divisible by 3.

and C denotes numbers divisible by 5.

$|A| =\bigg[\dfrac{60}{2}\bigg]=30 \\ |B| =\bigg[\big[\dfrac{60}{3}\big]\bigg]=20 \\ |C| =\bigg[\big[\dfrac{60}{5}\big]\bigg]=12$

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

$|AՈC| =\bigg[\big[\dfrac{60}{2\times5}\big]\bigg]=6$

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

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

$|A ̅ՈB ̅ՈC ̅|=60-(30+20+12)+(10+6+4)-2=60-62+20-2=16$

This shows 16 numbers are not divisible by 2, 3 0r 5.

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.