Three-set Venn diagram problems

Question 1 of 10

In a class of 58 pupils, 28 study French (F), 23 study Twi (T) and 29 study Ewe (E). 10 study F and T, 12 study F and E, 13 study T and E, and 6 study all three. How many study none of the three languages?

Question 2 of 10

In a class of 48 pupils, 24 study French (F), 20 study Twi (T) and 26 study Ewe (E). 8 study F and T, 11 study F and E, 8 study T and E, and 5 study all three. How many study exactly two of the languages?

Question 3 of 10

In a class of 35 pupils, 17 study French (F), 17 study Twi (T) and 16 study Ewe (E). 7 study F and T, 7 study F and E, 9 study T and E, and 4 study all three. How many study French only?

Question 4 of 10

A′ ∩ B means

Question 5 of 10

If A ⊂ B, then A ∪ B equals

Question 6 of 10

In a survey of 39 farmers, 20 grow maize (M), 16 grow cassava (C) and 19 grow yam (Y). 8 grow M and C, 9 grow M and Y, 4 grow C and Y, and 2 grow all three. (a) Draw a Venn diagram. (b) How many grow maize only? (c) How many grow none of the crops?

Question 7 of 10

n(A ∪ B) can be greater than n(A) + n(B).

Question 8 of 10

In a group of 48 people, 16 like tea, 40 like coffee and 13 like both. The number who like neither is ___.

Question 9 of 10

In a class of 68 pupils, 36 study French (F), 34 study Twi (T) and 25 study Ewe (E). 14 study F and T, 13 study F and E, 14 study T and E, and 6 study all three. How many study French only?

Question 10 of 10

If A and B are disjoint, n(A ∩ B) = 0.