Question

1. - / 1 points details my notes ask your teacher practice another if ( n(a) = 27 ), ( n(b) = 24 ), ( n(c) = 21 ), ( n(a cap b) = 6 ), ( n(a cap c) = 8 ), ( n(b cap c) = 4 ), and ( n(a cup b cup c) = 55 ), find ( n(a cap b cap c) ). tanfin11 6.2.016 resources ebook submit answer 8. - / 2 points details my notes ask your teacher practice another tanfin11 6.2.018 a survey of 3000 subscribers to a certain news paper revealed that 2700 people subscribe to the daily morning edition and 1500 subscribe to both the daily and the sunday editions. how many subscribe to the sunday edition? people how many subscribe to the sunday edition only? people resources ebook

Explanation:

Problem 7

Step1: Recall union formula

$$n(A \cup B \cup C) = n(A) + n(B) + n(C) - n(A \cap B) - n(A \cap C) - n(B \cap C) + n(A \cap B \cap C)$$

Step2: Rearrange for unknown

$$n(A \cap B \cap C) = n(A \cup B \cup C) - n(A) - n(B) - n(C) + n(A \cap B) + n(A \cap C) + n(B \cap C)$$

Step3: Substitute given values

$$n(A \cap B \cap C) = 55 - 27 - 24 - 21 + 6 + 8 + 4$$

Step4: Calculate the result

$$n(A \cap B \cap C) = 55 - 72 + 18 = 1$$

Step1: Define given values

Let $n(U)=3000$, $n(\text{Daily})=2700$, $n(\text{Daily} \cap \text{Sunday})=1500$. Assume all are subscribers to at least one edition, so $n(\text{Daily} \cup \text{Sunday})=3000$.

Step2: Find total Sunday subscribers

Use union formula: $n(\text{Daily} \cup \text{Sunday}) = n(\text{Daily}) + n(\text{Sunday}) - n(\text{Daily} \cap \text{Sunday})$
Rearrange: $n(\text{Sunday}) = n(\text{Daily} \cup \text{Sunday}) - n(\text{Daily}) + n(\text{Daily} \cap \text{Sunday})$
Substitute values: $n(\text{Sunday}) = 3000 - 2700 + 1500 = 1800$

Step3: Find Sunday-only subscribers

Subtract overlap from total Sunday: $n(\text{Sunday only}) = n(\text{Sunday}) - n(\text{Daily} \cap \text{Sunday})$
Substitute values: $n(\text{Sunday only}) = 1800 - 1500 = 300$

Answer:

1

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Problem 8