In a group of 15,7 have studied Latin, 8 have studied Greek, and 3 have not studied either.How many of these studied both Latin and Greek

One Answer on this Question

1. Given:

   In a group of 15 students,

   7 have studied Latin,

   8 have studied Greek,

   3 have not studied either.

   To find:

   The number of students who studied both Latin and Greek.

   Solution:

   In a group of 15 students, have studied Latin, 8 have studied Greek, 3 have not studied either.

   Therefore,

   n(A∪B) = 15 – 3

   n(A∪B) = 12

   7 have studied Latin,

   n(A) = 7

   8 have studied Greek,

   n(B) = 8

   n(A∩B) is the number of students who studied both Latin and Greek.

   n(A∩B) = n(A) + n(B) – n(A∪B)

   n(A∩B) = 7 + 8 – 12

   n(A∩B) = 15 – 12

   n(A∩B) = 3

   The number of students who studied both Latin and Greek is 3

   Final answer:

   3 of them studied both Latin and Greek.

   Thus, the correct answer .3

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