Question 5 (12 points)
Given the following cardinalities: , and , find the
following:

if , find .

if , find .

Ask by Weston Donnelly. in the United States

Jan 22,2025

Question

Question 5 (12 points)
Given the following cardinalities: , and , find the
following:

if , find .

if , find .

Ask by Weston Donnelly. in the United States

Jan 22,2025

UpStudy AI · Accepted Answer

Let's solve each part step-by-step using the principles of set theory.

### **1. Finding $$ n(A \cup B) $$ when $$ n(A \cap B) = 47 $$**

The formula for the union of two sets is:
$$
n(A \cup B) = n(A) + n(B) - n(A \cap B)
$$

Plugging in the given values:
$$
n(A \cup B) = 81 + 66 - 47 = 147 - 47 = 100
$$

**Answer:** $$ n(A \cup B) = 100 $$

---

### **2. Finding $$ n(A \cap B) $$ when $$ n(A \cup B) = 147 $$**

Using the same formula:
$$
n(A \cup B) = n(A) + n(B) - n(A \cap B)
$$
$$
147 = 81 + 66 - n(A \cap B)
$$
$$
147 = 147 - n(A \cap B)
$$
$$
n(A \cap B) = 0
$$

**Answer:** $$ n(A \cap B) = 0 $$

This means that sets $$ A $$ and $$ B $$ are **disjoint**, having no elements in common.

---

### **Summary:**
1. $$ n(A \cup B) = 100 $$
2. $$ n(A \cap B) = 0 $$
1. $$ n(A \cup B) = 100 $$ 2. $$ n(A \cap B) = 0 $$

Question 5 (12 points)
Given the following cardinalities: , and , find the
following:

if , find .

if , find .

Upstudy AI Solution

Answer

Solution

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Question 5 (12 points) Given the following cardinalities: , and , find the following: if , find . if , find .

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Question 5 (12 points)
Given the following cardinalities: , and , find the
following:

if , find .

if , find .