Answer + Step-by-step explanation:
let R be the set of farmers cultivating rice.
let W be the set of farmers cultivating wheat.
let n be the total number of farmers.
i) Check the attachment.
ii) Card R∪W = Card R + Card W - Card R∩W
Note : Card R denotes the number of farmers cultivating rice.
[tex]CardR\cup W=n-\frac{20}{100} n = \frac{80}{100} n[/tex]
[tex]CardR=\frac{70}{100} n[/tex]
[tex]CardW=\frac{60}{100}n[/tex]
[tex]CardR \cap W=450[/tex]
Card R∪W = Card R + Card W - Card R∩W
[tex]\Longleftrightarrow \frac{80}{100} n=\frac{70}{100} n + \frac{60}{100} n-450[/tex]
[tex]\Longleftrightarrow \frac{50}{100} n=450[/tex]
[tex]\Longleftrightarrow n= 2 \times 450 = 900[/tex]
iiI) the number of farmers who are cultivating rice only :
[tex]900\times \frac{70}{100} -450=180[/tex]
