venn diagram

Front

What is a Venn diagram?

Back

A Venn diagram is a visual representation that shows the relationships between different sets, using overlapping circles to illustrate commonalities and differences.

Front

What does the shaded region in a Venn diagram represent?

Back

The shaded region represents the elements that belong to the specified sets, depending on the context (e.g., A or B, A and B).

Front

How do you find the number of elements in the union of two sets A and B?

Back

The number of elements in the union of two sets A and B is found using the formula: |A U B| = |A| + |B| - |A ∩ B|.

Front

What does the symbol A ∩ B represent in a Venn diagram?

Back

A ∩ B represents the intersection of sets A and B, which includes all elements that are common to both sets.

Front

What does the symbol A' represent in a Venn diagram?

Back

A' represents the complement of set A, which includes all elements that are not in set A.

Front

If a Venn diagram shows 50 students who play football and 30 who play wrestling, and 10 play both, how many play either football or wrestling?

Back

Using the formula |A U B| = |A| + |B| - |A ∩ B|, we find |A U B| = 50 + 30 - 10 = 70 students.

Front

How can you determine how many students do not belong to either of the sets in a Venn diagram?

Back

To find the number of students not in either set, subtract the total number of students in the union of the sets from the total number of students surveyed.

Front

What is the purpose of using a Venn diagram in problem-solving?

Back

Venn diagrams help visualize relationships between sets, making it easier to understand overlaps, differences, and total counts.

Front

In a Venn diagram, if set A has 20 elements and set B has 15 elements with 5 elements in both, how many elements are in A or B?

Back

|A U B| = |A| + |B| - |A ∩ B| = 20 + 15 - 5 = 30 elements.

Front

What does it mean if two circles in a Venn diagram do not overlap?

Back

If two circles do not overlap, it means that the two sets are disjoint, meaning they have no elements in common.