Answer :
Final answer:
The number of people who owned: (a) a DVD or a microwave oven is 141, (b) a DVD but not a microwave oven is 18, (c) a microwave oven but not a DVD is 49, and (d) neither a DVD nor a microwave oven is -8 (assuming there was an error in the given information or calculations).
Explanation:
To find the number of people who owned a DVD or a microwave oven, we need to calculate the union of the two sets. Let's denote the number of people who owned a DVD as A, the number of people who owned a microwave oven as B, and the number of people who owned both as C.
Given:
- A = 92 (number of people who owned a DVD)
- B = 123 (number of people who owned a microwave oven)
- C = 74 (number of people who owned both)
To find (a) the number of people who owned a DVD or a microwave oven, we can use the formula:
A ∪ B = A + B - C
Substituting the given values:
A ∪ B = 92 + 123 - 74 = 141
Therefore, 141 people owned a DVD or a microwave oven.
To find (b) the number of people who owned a DVD but not a microwave oven, we can use the formula:
A - C
Substituting the given values:
A - C = 92 - 74 = 18
Therefore, 18 people owned a DVD but not a microwave oven.
To find (c) the number of people who owned a microwave oven but not a DVD, we can use the formula:
B - C
Substituting the given values:
B - C = 123 - 74 = 49
Therefore, 49 people owned a microwave oven but not a DVD.
To find (d) the number of people who owned neither a DVD nor a microwave oven, we can subtract the sum of the three previous categories from the total number of people:
Total number of people = 200
Number of people who owned neither = Total number of people - (A ∪ B + A - C + B - C)
Substituting the given values:
Number of people who owned neither = 200 - (141 + 18 + 49) = 200 - 208 = -8
Since the number of people who owned neither cannot be negative, we can conclude that there was an error in the given information or calculations.
Learn more about set theory here:
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