2. Use the addition principle for counting tq solve the following. If $$ n(A)=5, n(B)=11 $$, and $$ n(A \cap B)=3 $$, what is $$ n(A \cup B) $$ ?

Question

UpStudy AI · Accepted Answer

To find $$ n(A \cup B) $$, we can use the addition principle for counting, which states:

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

Given the values:
- $$ n(A) = 5 $$
- $$ n(B) = 11 $$
- $$ n(A \cap B) = 3 $$

We can substitute these values into the formula:

$$
n(A \cup B) = 5 + 11 - 3
$$

Calculating this gives:

$$
n(A \cup B) = 16 - 3 = 13
$$

Thus, the number of elements in the union of sets $$ A $$ and $$ B $$ is

$$
\boxed{13}
$$
$$ n(A \cup B) = 13 $$

Use the addition principle for counting tq solve the following. If , and
, what is ?