Chapter 3 HW-Probability Topics Current score: $$ { }^{+} $$À Category: Homework 3/100 points Submit assignment 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 $$ \begin{array}{llll}37 & 38 & 39 & 40\end{array} $$ Current learning objective: Terminology Question 2 Practice similar questions Prev Next Score: 0 of 1 point If A and B are two sets such that $$ n(A \cup B)=100, n(A)=32 $$, and $$ n(B)=72 $$. How many elements does $$ A \cap B $$ have? Enter your answer

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UpStudy AI · Accepted Answer

To find the number of elements in the intersection of sets $$ A $$ and $$ B $$ (i.e., $$ A \cap B $$), we can use the principle of inclusion-exclusion for sets:

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

Given:
- $$ n(A \cup B) = 100 $$
- $$ n(A) = 32 $$
- $$ n(B) = 72 $$

Plugging in the values:

$$
100 = 32 + 72 - n(A \cap B)
$$

$$
100 = 104 - n(A \cap B)
$$

Solving for $$ n(A \cap B) $$:

$$
n(A \cap B) = 104 - 100 = 4
$$

**Answer:**  
4
$$ A \cap B $$ has 4 elements.

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