How to Find Intersection and Union of Two Intervals

TL;DR

To find the intersection of two intervals, graph them and identify the overlapping region, including values present in both. For the union, combine the intervals to encompass all values from the start to the end, noting open and closed circles as needed. This method only applies when the intervals intersect.

Transcript

in this video we're going to talk about how to find the intersection and the union of the intervals shown here so this symbol that's intersection and this symbol means union so let's begin let's graph each interval separately first so two to five we'll say this is two and this is five we have an open circle at two since uh we have a parenthesis the... Read More

Key Insights

• 😚 Graphing intervals involves using open and closed circles to indicate the inclusion or exclusion of values.
• ❓ The intersection of intervals can be found by identifying the overlapping region and including common values.
• ❤️‍🩹 The union of intervals is obtained by combining the intervals and including all values from the start to the end.
• 💦 The technique shown in the video only works if there is an intersection between the intervals.
• 🇪🇺 The inclusion of endpoints in the intersection or union depends on whether the values exist in both intervals.
• 🫥 Understanding interval notation (parentheses and brackets) is crucial in correctly representing intervals on a number line.
• 🇪🇺 The process of finding the intersection and union of intervals can be applied to various examples and scenarios.

Questions & Answers

Q: How do you graph intervals on a number line?

Intervals can be graphed on a number line by indicating open circles for values not included and closed circles for values included in the interval. Parentheses and brackets determine whether the circles are open or closed.

Q: What is the intersection of two intervals?

The intersection of two intervals is the region where they overlap. To find the intersection, identify the common values between the intervals and include them. Use closed circles for values included in both intervals and open circles for values included in one interval but not the other.

Q: Can you include endpoints in the intersection of intervals?

Endpoints can be included in the intersection if they exist in both intervals. For example, if both intervals include the value 3, a closed circle is used at 3 to indicate its inclusion in the intersection.

Q: How do you find the union of two intervals?

To find the union of two intervals, combine them and include all the values from the starting point to the ending point. Use the notation of the original intervals to indicate open or closed circles for the endpoints.

Summary & Key Takeaways

• The video demonstrates how to graph intervals on a number line by indicating open and closed circles based on parentheses and brackets.

• The intersection of two intervals is found by identifying the overlapping region and including the values that exist in both intervals.

• The union of two intervals is obtained by combining the intervals and including all the values from the starting point to the ending point.