Question

Construct a Venn diagram illustrating the given sets. A={15,19,23,31},B={3,7,15,19,23,27}, C={11,15,27},U={3,7,11,15,19,23,27,31,35}

Answer 1

A Venn diagram is constructed by drawing a large rectangle for the universal set U, and within it, overlapping circles for each set A, B, and C. Place shared elements in intersecting areas and unique elements in non-overlapping parts of the circles.

Step-by-step explanation:

To construct a Venn diagram with the given sets, A, B, and C, within the universal set U, follow these steps:

1. Draw a large rectangle to represent the universal set U which includes all possible elements. In this case, U={3,7,11,15,19,23,27,31,35}.
2. Inside this rectangle, draw three overlapping circles or ovals to represent the sets A, B, and C.
3. Write the elements of each set in the appropriate region of the Venn diagram, making sure that shared elements are placed in the intersections of the circles. For example, the element 15 is shared by all three sets, so it should be placed in the area where all three circles overlap.
4. Any elements that are not shared (unique to one set) should be placed in the non-overlapping parts of the corresponding circle.
5. After all elements are placed, you can easily visualize the relationships between the sets, such as which elements are unique to a set, and which are shared among two or all three sets.

Here's an example of how the central part of the Venn diagram could be filled out:

• A AND B: {15,19,23}
• B AND C: {27}
• A AND C: {15}
• A OR B: {3,7,15,19,23,27,31}

Remember that the areas that don't overlap with any other set should also have the unique elements of those sets written in.