Core Mathematics

1(A ∪ B)′ = A′ ∩ B′.

2In 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?

3In a class of 60 pupils, 26 study French (F), 23 study Twi (T) and 27 study Ewe (E). 10 study F and T, 8 study F and E, 8 study T and E, and 4 study all three. How many study exactly two of the languages?

4In a group of 55 people, 16 like tea, 36 like coffee and 4 like both. The number who like neither is ___.

5A ∩ A′ = U.

6In 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?

7If A ⊂ B, then A ∪ B equals

8In a class of 47 pupils, 17 study French (F), 22 study Twi (T) and 24 study Ewe (E). 6 study F and T, 9 study F and E, 6 study T and E, and 2 study all three. How many study none of the three languages?

9In a class of 56 pupils, 31 study French (F), 27 study Twi (T) and 27 study Ewe (E). 14 study F and T, 9 study F and E, 13 study T and E, and 6 study all three. How many study French only?

10In a group of 44 people, 38 like tea, 16 like coffee and 13 like both. The number who like neither is ___.