Question

the diagram shows the universal set u of all parallelograms. set a represents parallelograms with four congruent sides, while b represents parallelograms with four congruent angles. how many of the parallelograms fall into the category ( a cup b )? 18 6 26 8

Explanation:

Step1: Recall the formula for union of sets

The formula for the number of elements in \( A \cup B \) is \( n(A \cup B)=n(A)+n(B)-n(A \cap B) \), where \( n(A) \) is the number of elements in set \( A \), \( n(B) \) is the number of elements in set \( B \), and \( n(A \cap B) \) is the number of elements in the intersection of \( A \) and \( B \).

Step2: Identify the values from the Venn diagram

From the Venn diagram:

• The number of elements only in \( A \) is \( 12 \), and the number of elements in \( A \cap B \) is \( 8 \), so \( n(A)=12 + 8=20 \).
• The number of elements only in \( B \) is \( 6 \), and the number of elements in \( A \cap B \) is \( 8 \), so \( n(B)=6 + 8 = 14 \).
• \( n(A \cap B)=8 \).

Step3: Calculate \( n(A \cup B) \)

Using the formula \( n(A \cup B)=n(A)+n(B)-n(A \cap B) \), substitute the values:
\( n(A \cup B)=(12 + 8)+(6 + 8)-8 \) or alternatively, we can sum the elements in \( A \) only, \( B \) only, and the intersection. So \( n(A \cup B)=12+8 + 6=26 \).

Answer:

26