Venn Diagrams

Front

What is a Venn Diagram?

Back

A Venn Diagram is a visual representation of the relationships between different sets, often using overlapping circles to show commonalities and differences.

Front

What does the intersection of two sets in a Venn Diagram represent?

Back

The intersection of two sets represents the elements that are common to both sets.

Front

How do you determine the number of elements that belong to only one set in a Venn Diagram?

Back

To find the number of elements that belong to only one set, subtract the number of elements in the intersection from the total number of elements in that set.

Front

If set A has 10 elements and set B has 5 elements, and they have 2 elements in common, how many elements are in A or B?

Back

The number of elements in A or B is calculated as |A| + |B| - |A ∩ B| = 10 + 5 - 2 = 13.

Front

What does the union of two sets in a Venn Diagram represent?

Back

The union of two sets represents all the elements that are in either set, including those that are in both.

Front

How can you represent the number of students who have brown hair OR wear glasses using a Venn Diagram?

Back

You add the number of students in set B (brown hair) and set G (glasses), then subtract the number of students in the intersection (both brown hair and glasses).

Front

In a Venn Diagram, if 16 students have brown hair and 3 students have both brown hair and glasses, how many students have only brown hair?

Back

To find the number of students with only brown hair, subtract the intersection from the total in set B: 16 - 3 = 13.

Front

What is the formula to find the number of elements in the union of two sets?

Back

The formula is |A ∪ B| = |A| + |B| - |A ∩ B|.

Front

If 39 senior boys play football or wrestle, and 9 play both, how many play only football or only wrestle?

Back

To find the number of students who play only football or only wrestle, subtract the number who play both from the total: 39 - 9 = 30.

Front

What is the significance of the area outside the circles in a Venn Diagram?

Back

The area outside the circles represents elements that do not belong to either of the sets being compared.