BECE Questions on Venn Diagram
BECE Questions on Venn Diagram
1. (a) In a school of 255 students, 80 of them study Arabic only and 125 study French only. Each student studies at least one of the two subjects
(i) Draw a Venn diagram to represent the information
(ii) How many students study?
(α) both subjects?
(β) French?
2. A and B are subsets of a universal set
U = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18}
Such that A = {even numbers} and B = {multiples of 3}
(i) List the elements of the sets A, B, (A∩B), (AUB) and (AUB)′
(ii) Illustrate the information in (i) on a Venn diagram
3. E and F are subsets of the universal set U such that
U = {natural numbers less than 15},
E = {even numbers between 1 and 15} and
F = {multiples of 4 between 9 and 15}.
(i) List the elements of U, E and F
(ii) Draw a Venn diagram to show the sets U, E and F
4. There are 30 boys in a sporting club. 20 of them play hockey and 15 play volley-ball. Each boy plays at least one of the two games.
(i) Illustrate the information on a Venn diagram.
(ii) How many boys play volley-ball only?
5. ε = {1, 2, 3, 4, …,18}
A = {Prime numbers}
B = {Odd numbers greater than 3}
(a) If A and B are subsets of the Universal set, ε, list the members of A and B
(b) Find the set
(i) A ∩ B;
(ii) A ∪ B
(c) (i) Illustrate ε, A and B on a Venn diagram.
(ii) Shade the region for prime factors of 18 on the Venn diagram
6. (a) M is a set consisting of all positive integers between 1 and 10. P and Q are subsets of M such that
P = {factors of 6}, Q = {multiples of 2}
(i) List the elements of M, P and Q
(ii) Represent M, P and Q on a Venn diagram
(iii) Find P ∩ Q
7. In the Venn diagram Q is the set of numbers inside the circle and R is the set of numbers inside the triangle
Find Q ∩ R
8. There are 20 students in a hostel. 16 of them are fluent in French and 10 of them are fluent in English. Each student is fluent in at least one of the two languages
(i) Illustrate this information on a Venn diagram
(ii) How many students are fluent in both English and French?
9. In a class of 60 students, 46 passed Mathematics and 42 passed English language. Everybody passed at least one of the two subjects.
(i) Illustrate this information on a Venn diagram
(ii) How many students passed in both subjects?
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