Question

Assume that 350 students are surveyed with the following results: 168 live in the west. 163 live in a large city. 179 are married. 77 live in the west in a large city. 79 are married and live in a large city. 89 are married and live in the west. 42 are married and live in a large city in the west. How many are unmarried, do not live in a large city, and do not live in the west?

Answer 1

To find the number of students who are unmarried, do not live in a large city, and do not live in the west, we need to subtract the number of students who satisfy any of these conditions from the total number of students surveyed.

Step-by-step explanation:

To find the number of students who are unmarried, do not live in a large city, and do not live in the west, we need to subtract the number of students who satisfy any of these conditions from the total number of students surveyed. Let's denote the number of students who satisfy each condition as follows:

• A = number of students who live in the west
• B = number of students who live in a large city
• C = number of students who are married

Using this notation, the number of students who are unmarried, do not live in a large city, and do not live in the west can be calculated as:

Total number of students surveyed - (A + B + C - (A ∩ B) - (B ∩ C) - (A ∩ C) + (A ∩ B ∩ C))

Substituting the given values, we have:

350 - (168 + 163 + 179 - 77 - 79 - 89 + 42) = 350 - 207 = 143

Therefore, there are 143 students who are unmarried, do not live in a large city, and do not live in the west.