Answer to Question #318655 in Discrete Mathematics for Ver

Question

In a large region, there are 450 farmers. 250 pounds of farm beetroot, 110 pounds of farm yams, 75 pounds of farm radish, 45 pounds of farm beetroot and radish, 40 pounds of farm yams and radish, and 30 pounds of farm beetroot and yams Let B, Y, and R represent the farms that grow beets, yams, and radish, respectively.

Determine the number of farmers that farm beetroot, yams, and radish.

Answer 1

$|B\cup Y\cup R|=|B|+|Y|+|R|-\\-|B\cap Y|-|Y\cap R|-|B\cap R|+|B\cap Y\cap R|.$

Here $B\cup Y\cup R-$ farmers that grow beetroot or yams or radish, $|B\cup Y\cup R|=450;$

$B\cap Y-$ ​​farmers that grow beetroot and yams, $|B\cap Y|=30$;

$Y\cap R-$ ​​farmers that grow yams and radish,$|Y\cap R|=40;$

$B\cap R-$ ​​farmers that grow beetroot and radish, $|B\cap R|=45;$

$B\cap Y\cap R-$ ​​ farmers that grow beetroot, yams and radish.

So,

$450=250+110+75-30-40-45+|B\cap Y\cap R|,\\ |B\cap Y\cap R|=130.$