Let $$ S=\{1,2,3, \ldots, 18,19,20\} $$ be the universal set. Let sets $$ A $$ and $$ B $$ be subsets of $$ S $$, where: Set $$ A=\{1,2,3,6,10,11,12,13,14,15,16,17\} $$ Set $$ B=\{7,9,10,16,18,19,20\} $$ Determine the following: $$ n(A)= $$ $$ n(\bar{A})= $$ $$ n(B)= $$ $$ n(A \cap B)= $$ $$ n(A \cup B)= $$

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**Step 1. Determine $$ n(A) $$:**

Set $$ A = \{1, 2, 3, 6, 10, 11, 12, 13, 14, 15, 16, 17\} $$.

Count the elements:

$$
n(A) = 12
$$

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**Step 2. Determine $$ n(\bar{A}) $$:**

The universal set $$ S $$ has 20 elements. Thus,

$$
n(\bar{A}) = n(S) - n(A) = 20 - 12 = 8
$$

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**Step 3. Determine $$ n(B) $$:**

Set $$ B = \{7, 9, 10, 16, 18, 19, 20\} $$.

Count the elements:

$$
n(B) = 7
$$

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**Step 4. Determine $$ n(A \cap B) $$:**

Find the intersection by identifying common elements in $$ A $$ and $$ B $$:

The common elements are $$ \{10, 16\} $$.

$$
n(A \cap B) = 2
$$

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**Step 5. Determine $$ n(A \cup B) $$:**

Using the formula for the union of two sets:

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

Substitute the known values:

$$
n(A \cup B) = 12 + 7 - 2 = 17
$$
- $$ n(A) = 12 $$ - $$ n(\bar{A}) = 8 $$ - $$ n(B) = 7 $$ - $$ n(A \cap B) = 2 $$ - $$ n(A \cup B) = 17 $$

Let be the universal set.
Let sets and be subsets of , where:
Set
Set
Determine the following:

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Let be the universal set. Let sets and be subsets of , where: Set Set Determine the following: