In a group of 50 people, 30 like dogs, 25 like cats, and 10 like both. How many

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Question: In a group of 50 people, 30 like dogs, 25 like cats, and 10 like both. How many people do not like either dogs or cats?

Options:

Correct Answer: 10

Solution:

The number of people who like either dogs or cats is 30 + 25 - 10 = 45. Therefore, those who do not like either is 50 - 45 = 5.

In a group of 50 people, 30 like dogs, 25 like cats, and 10 like both. How many people do not like either dogs or cats?

In a group of 50 people, 30 like dogs, 25 like cats, and 10 like both. How many people do not like either dogs or cats?

Step 1: Identify the total number of people in the group, which is 50.
Step 2: Identify how many people like dogs, which is 30.
Step 3: Identify how many people like cats, which is 25.
Step 4: Identify how many people like both dogs and cats, which is 10.
Step 5: Calculate the number of people who like either dogs or cats using the formula: (people who like dogs) + (people who like cats) - (people who like both). This gives us 30 + 25 - 10 = 45.
Step 6: To find out how many people do not like either dogs or cats, subtract the number of people who like either from the total number of people: 50 - 45 = 5.

Set Theory – Understanding how to calculate the union of two sets and account for overlaps.
Inclusion-Exclusion Principle – Applying the principle to avoid double counting individuals who like both dogs and cats.