Ex. 6. In a group of 15 people, 7 read French, 8 read English while 3 of them read none of these two. How many of them read French and English both?
Sol. Let circles x and y represent people who read French and English, respectively.
Area A shows the people who read French only.
Area C shows the people who read English only.
Area B shows the people who read French and English both.
(A + B + C) + 3 = 15 or A + B + C = 12 … (i)
A + B = 7, B + C = 8
Adding these two, we get A + 2B + C = 15 … (ii)
Subtracting (i) from (ii), we get
B = 15 – 12 = 3
Therefore, number of people who read French and English both is 3.
Hence, the correct answer is (b).