Out of a group of 50 persons, 32 take eggs, 25 take meat and 15 take both eggs and meat.
How many of them are pure vegetarians?
Answers
Sets
Total number of persons in the group = 50
Number of persons who take eggs = n( E ) = 32
Number of persons who take meat = n( M ) = 25
Number of persons who take both eggs and meat = n( E ∩ M ) = 15
Number of persons who take eggs or meat [ i.e Number of non - vegetarians ] = n( E ∪ M ) = ?
Using the relation between two sets we get,
⇒ n( E ∪ M ) = n( E ) + n ( M ) - n( M ∩ N )
Substituting the values we get,
⇒ n( E ∪ M ) = 32 + 25 - 15
⇒ n( E ∪ M ) = 57 - 15
⇒ n( E ∪ M ) = 42
∴ Total number of non - vegetarians = 42
Hence, Number of pure vegetarians = Total number of persons - Total number of non - vegetarians = 50 - 42 = 8
∴ there are 8 pure vegetarians in the given group of 50 persons.
: Given :
Egg = n(E)=32
meat = n(M)=25
Egg and meat =n(E ⋃ M)=15
Total person = 50
★ To find,
→ Pure vegetarian=?
† Formula
n(E ⋃ M)= n(E)+n(M)-n(E ⋃ M)
Now,
→ n(E ⋃ M)= 32+25-15
→ n(E ⋃ M) = 57-15
→ n(E ⋃ M) = 42
→for vegetarian= total person - non vegetarian
→ Vegetarian = 50-42
→ vegetarian = 8
Hence,
★ in 50 person their are 8 vegetarian person and remaining 42 are non vegetarian.