In a class, 120 students speak English or French or both. 70 speak English and 55 speak french. how many speak English but not French?
n(E n F)= n(E)+n(F) - n(£)
=(70+55) - 120
=5
n(E n F')=n(E) - n(E n F)
=70-5
=65
120 - (70 + 55) = ?
To find the number of students who speak English but not French, we can subtract the number of students who speak both English and French from the total number of students who speak English.
Let's denote:
E = number of students who speak English
F = number of students who speak French
E∩F = number of students who speak both English and French
Given that there are 70 students who speak English (E = 70) and 55 students who speak French (F = 55), we can calculate the number of students who speak both English and French using the formula:
E∩F = E + F - Total
Substituting the given values into the formula:
E∩F = 70 + 55 - 120
E∩F = 125 - 120
E∩F = 5
Now, to find the number of students who speak English but not French, we subtract the number of students who speak both English and French (E∩F) from the total number of students who speak English (E):
English Only = E - E∩F
English Only = 70 - 5
English Only = 65
Therefore, 65 students speak English but not French.
To find out how many students speak English but not French, you can use a method called Venn diagram. Let's break down the information given:
- 120 students speak English or French or both.
- 70 students speak English.
- 55 students speak French.
To start, draw two overlapping circles representing English and French.
Next, label the overlapping region where the circles intersect as the number of students who speak both English and French.
Inside the English circle, write "70" to represent the 70 students who speak English. Then, inside the French circle, write "55" to represent the 55 students who speak French.
Since the sum of students speaking English and students speaking French is 120 (70 + 55), write "120" where the circles overlap to represent the total number of students in the class.
Now, to find the number of students who speak only English, subtract the number of students who speak both English and French (which is already labeled in the overlapping region) from the total number of English speakers (70).
So, to find the number of students who speak English but not French:
70 (total English speakers) - number of students who speak both English and French (labeled in the overlap) = Answer
Finally, calculate the difference:
70 - 55 = 15
So, 15 students speak English but not French.