Final answer:
The question appears to contain a mistake because subtracting the number of students who failed both subjects from the number who passed math results in a negative number, which is not feasible. To solve this with set theory and provide a correct number of students who passed science or passed both, more information or corrected data is required.
Step-by-step explanation:
We are asked to find how many students passed in science and how many passed both science and maths. To approach this problem, we need to use the principles of set theory, particularly focusing on the complement and intersection of sets (passed and failed subjects). Let's denote the number of students who passed maths as P(M), failed maths as F(M), and failed both sciences as F(Both).
Givens:
- P(M) = 80
- F(M) = 70
- F(Both) = 90
Since 90 students failed both subjects, this is a subset of those who failed maths. Therefore, the total number of students is F(M) plus the number of students who passed maths but did not fail science. We can calculate this as P(M) - F(Both), which results in 80 - 90 = -10. This negative number is not realistic, indicating error in the available options or question. The correct calculation should provide a non-negative total number of students who passed science, which is not reflected in the answer choices given (a, b, c, d).
Therefore, either the question is flawed, or more information is required to render a proper solution.