In a survey of 150 people, 90 like dogs, 60 like cats, and 30 like both. How man

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Question: In a survey of 150 people, 90 like dogs, 60 like cats, and 30 like both. How many people like neither dogs nor cats?

Options:

Correct Answer: 30

Solution:

Using inclusion-exclusion, the number of people who like either is 90 + 60 - 30 = 120. Therefore, those who like neither is 150 - 120 = 30.

In a survey of 150 people, 90 like dogs, 60 like cats, and 30 like both. How many people like neither dogs nor cats?

In a survey of 150 people, 90 like dogs, 60 like cats, and 30 like both. How many people like neither dogs nor cats?

Step 1: Start with the total number of people surveyed, which is 150.
Step 2: Identify how many people like dogs, which is 90.
Step 3: Identify how many people like cats, which is 60.
Step 4: Identify how many people like both dogs and cats, which is 30.
Step 5: Use the inclusion-exclusion principle to find the number of people who like either dogs or cats. This is calculated as: 90 (like dogs) + 60 (like cats) - 30 (like both) = 120.
Step 6: To find out how many people like neither dogs nor cats, subtract the number of people who like either from the total number of people surveyed: 150 - 120 = 30.
Step 7: Therefore, the number of people who like neither dogs nor cats is 30.

Inclusion-Exclusion Principle – A method used to calculate the size of the union of multiple sets by including the sizes of the individual sets and excluding the sizes of their intersections.
Set Theory – The study of collections of objects, which in this case involves determining the relationships between people who like dogs, cats, or both.