Out of the 40 students in a class of 22 take Chemistry and 17 take physics. If 8 students take both Chemistry and Physics, determine the number of students that take neither Physics nor Chemistry.
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Let's solve this problem using set theory principles.
Let C be the set of students who take Chemistry.
Let P be the set of students who take Physics.
We are given the following information:
Total number of students = 40
Number of students who take Chemistry, n(C) = 22
Number of students who take Physics, n(P) = 17
Number of students who take both Chemistry and Physics, n(C ∩ P) = 8
We need to find the number of students who take neither Physics nor Chemistry.
Step 1: Determine the number of students who take Chemistry or Physics or both.
The formula for the union of two sets is:
n(C ∪ P) = n(C) + n(P) - n(C ∩ P)
Substitute the given values into the formula:
n(C ∪ P) = 22 + 17 - 8
n(C ∪ P) = 39 - 8
n(C ∪ P) = 31
So, 31 students take at least one of the subjects (Chemistry or Physics).
Step 2: Determine the number of students who take neither Physics nor Chemistry.
To find the number of students who take neither subject, subtract the number of students who take at least one subject from the total number of students.
Number of students taking neither = Total number of students - n(C ∪ P)
Number of students taking neither = 40 - 31
Number of students taking neither = 9
The number of students that take neither Physics nor Chemistry is 9.