A set is simply the group of related item.
- 20 villagers that eat both
- 650 villagers that eat only one
Let:
[tex]C \to[/tex] Those who eat corn
[tex]M \to[/tex]Those who eat millet
[tex]x \to[/tex] Those who eat both
So, we have:
[tex]C = 400[/tex]
[tex]M= 290[/tex]
[tex]None = 60[/tex]
[tex]Total = 730[/tex]
(a) The number of those who eat both
To do this, we make use of the following equation
[tex]Total =C + M - x + None[/tex]
The above equation represents the sum of all possible subsets
So, we have:
[tex]730 =400 + 290 - x+ 60[/tex]
Collect like terms
[tex]x =400 + 290 + 60 -730[/tex]
[tex]x =20[/tex]
Hence, 20 villagers eat both
(b) Number of those that eat only one
We have:
[tex]C = 400[/tex]
[tex]M= 290[/tex]
The number (n) of those that eat only one is:
[tex]n =C -x+ M - x[/tex]
[tex]n = 400 - 20 + 290 - 20[/tex]
[tex]n =650[/tex]
Hence, 650 villagers eat only one
See attachment for the Venn diagram that illustrates the set
Read more about sets at:
https://brainly.com/question/6780543
