Subjects sets and logic

Tea Coffee Survey Ea412B

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1. **State the problem:** We have a survey of 180 people about their morning beverage choices: coffee only, tea only, both tea and coffee, or neither. 2. **Given data:** - Tea only = 64 - Coffee only = 56 - Both tea and coffee = 24 - Total people surveyed = 180 3. **Find:** - Number of people who drink tea in the morning - Number of people who drink coffee in the morning - Number of people who drink neither tea nor coffee 4. **Formula and rules:** - People who drink tea = Tea only + Both - People who drink coffee = Coffee only + Both - People who drink neither = Total - (Tea only + Coffee only + Both) 5. **Calculate number of people who drink tea:** $$\text{Tea} = 64 + 24 = 88$$ 6. **Calculate number of people who drink coffee:** $$\text{Coffee} = 56 + 24 = 80$$ 7. **Calculate number of people who drink neither:** $$\text{Neither} = 180 - (64 + 56 + 24) = 180 - 144 = 36$$ **Final answers:** - People who drink tea in the morning: $88$ - People who drink coffee in the morning: $80$ - People who drink neither tea nor coffee: $36$