Subset, strict subset, and superset | Probability and Statistics | Khan Academy

TL;DR

This video explains the concepts of sets, subsets, and supersets, illustrating with examples and providing notations for each.

Transcript

Let's define ourselves some sets. So let's say the set A is composed of the numbers 1. 3. 5, 7, and 18. Let's say that the set B-- let me do this in a different color-- let's say that the set B is composed of 1, 7, and 18. And let's say that the set C is composed of 18, 7, 1, and 19. Now what I want to start thinking about in this video is the noti... Read More

Key Insights

• 😫 Subset: A subset is a set where every member is also present in another set.
• 😫 Strict Subset: A strict or proper subset is a subset that is not equal to the larger set.
• 😫 Superset: A superset is a set that includes every element from another set.
• 🔙 B being a subset of A: Set B is a subset of set A because every element in B (1, 7, and 18) is also present in A.
• 🔙 A being a superset of B: A is a superset of B because it contains every element that is in B and might contain additional elements.
• 😫 Subset notation: A subset is denoted by writing the subset symbol (∈) between the two sets.

Questions & Answers

Q: What is a subset?

A subset is a set where every element is also a member of another set. In other words, all the elements in the subset are also present in the larger set.

Q: Is set B a subset of set A?

Yes, set B is a subset of set A. Every member of set B (1, 7, and 18) is also present in set A.

Q: Can set C be considered a subset of set A?

No, set C is not a subset of set A. While set C does have elements that are present in set A (18, 7, and 1), it also contains an additional element (19) that is not present in set A.

Q: What is a strict subset?

A strict or proper subset refers to a subset that is not equal to the larger set. In the video, it is denoted by crossing out the equal part of the less than or equal sign. Set B is a strict subset of set A because it contains elements from A but not all the elements of A.

Summary & Key Takeaways

• The video introduces sets A, B, and C, consisting of different numbers.

• A subset is a set where every element is also a member of another set.

• Set B is a subset of set A, but not equal to A, making it a strict or proper subset.