50 students sat for a test in Maths and English. If 14 passed in both subjects and 5 failed in both subjects… find how many students passed only English
Let A be the set of students who passed Maths and B the set of students who passed English.
We are given:
1. n(A ∩ B) = 14, meaning that 14 students passed both Maths and English.
2. The total number of students is 50.
3. 5 students failed both Maths and English, meaning that they are not in either set A or B.
We are looking for the number of students who passed only English: n(B-A).
To find n(B-A), we need to find n(B). We can do this using the Principle of Inclusion-Exclusion, which states that:
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
We know the number of students who passed at least one subject is 50 - 5 = 45, meaning:
n(A ∪ B) = 45.
We now have:
45 = n(A) + n(B) - 14, which can be simplified to:
n(A) + n(B) = 59
Unfortunately, we cannot continue without knowing how many students passed only Maths. The problem likely has omitted information. If the number of students who passed only Maths or only English were provided, we could solve for the respective missing values.