Applications of sets

Question

A survey of

500

farmers showed that of the​ farmers,

121

grew only​ wheat,

114

grew only​ corn,

89

grew only​ oats,

187

grew​ wheat,

53

grew wheat and​ corn,

45

grew wheat and​ oats, and

177

grew corn. Determine the number of farmers who ​a) grew at least one of the​ three, ​b) grew all​ three, ​c) did not grow any of the​ three, and ​d) grew exactly two of the three.

Answer 1

solve with a Venn diagram

draw a rectangle with 3 overlapping circles inside

answer to b) is where all 3 intersect =32

answer to c) is the area 500 minus what's inside all 3 circles =500-400- 100

a) 76

d) 44