Question

The diagram shows the universal set U = {parallelograms}. Set A represents parallelograms with four congruent angles .

How many of the parallelograms fall into the category A u B?

Answer 1

Answer: The number of parallelograms that fall into the category A ∪ B is 26.

Step-by-step explanation: The given diagram shows the universal set U defined by

U = {parallelograms}.

Set A represents parallelograms with congruent sides and set B represents parallelograms with four congruent angles.

We are to find the number of parallelograms that fall into the category A ∪ B.

From the diagram, we find that

`n(A)=12+8=20,\\\\n(B)=6+8=14,\\\\n(A\cap B)=8,\\\\n(A\cup B)=?`

From set theory, we have

`n(A\cup B)=n(A)+n(B)-n(A\cap B)=20+14-8=26.`

Thus, the number of parallelograms that fall into the category A ∪ B is 26.

Answer 2

26 is the number of the parallelograms that fall into the category A U B. In this universal set, you must likely to find 26 parallelograms that fall into the category A U B. With 4 congruent sides and four congruent angles in set A and B we can see 26 parallelograms that fall into the category A U B.