Concept Explanation: Union of Disjoint Sets

When two sets A and B are disjoint (meaning they have no elements in common), the number of elements in their union (A ∪ B) is simply the sum of the number of elements in each set.

Step-by-Step Solution:

Step 1: Identify the given values.

n(A) = 18
n(B) = 12
A ∩ B = ∅ (empty set), meaning n(A ∩ B) = 0

Step 2: Apply the formula for the union of two sets.

The general formula is: $n (A \cup B) = n (A) + n (B) - n (A \cap B)$

Step 3: Substitute the known values into the formula.

$n (A \cup B) = 18 + 12 - 0$

Step 4: Perform the calculation.

$n (A \cup B) = 30$

Final Answer: 30

Key Formulae and Theory:

Union of Two Sets: $n (A \cup B) = n (A) + n (B) - n (A \cap B)$

Disjoint Sets: Two sets are disjoint if they have no elements in common, i.e., $A \cap B = \emptyset$ . For disjoint sets, the formula simplifies to: $n (A \cup B) = n (A) + n (B)$

Concept Explanation: Union of Disjoint Sets

Step-by-Step Solution:

Related Topics:

Key Formulae and Theory: