Theory question 111
SetsIn a class of 40 students, 25 speak Hausa, 16 speak Igbo, 21 speak Yoruba and each of the students speaks at least one of these three languages. If 8 speak Hausa and Igbo, 11 speak Hausa and Yoruba and 6 speak Igbo and Yoruba
(a) Draw a Venn diagram to illustrate this information, using x to represent the number of students that speak all three;
(b) calculate the value of x.
Show the model answer
(a) Three overlapping circles H, I, Y in a rectangle of 40. Regions: H∩I only = 8 − x; H∩Y only = 11 − x; I∩Y only = 6 − x; centre = x; H only = 25 − (8 − x) − (11 − x) − x = 6 + x; I only = 2 + x; Y only = 4 + x
(b) Sum of regions = 40: (6 + x) + (2 + x) + (4 + x) + (8 − x) + (11 − x) + (6 − x) + x = 37 + x = 40
x = 3
Fill the centre first, then the pairs, then the 'only' regions.