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In the Introduction to sets video, we 
looked at what sets are, and discussed 

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things like set membership, and the various 
operations that we can perform on sets. 

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I finished that video by mentioning subsets and 
supersets. I didn't go into detail at the time, 

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because we'd had enough theory at that point.
In the next few videos, we'll see what subsets 

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and supersets are, and how we 
can test for them in Python. 

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This diagram represents two sets: a 
set of animals, and a set of birds. 

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Birds are also animals, and all of our 
birds are also members of the Animals set. 

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When all the items of one 
set are also in another set, 

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the contained set is called a 
subset of the containing set. 

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Here, Birds is a subset of Animals 
– as we can see on the next slide. 

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In set theory, that would be written as: 

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In Python, we use the less 
than or equal to symbol: 

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Birds is also a proper subset of Animals.
A proper subset is a subset that also isn't 

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equal to the set that contains it. The 
distinction is important, in set theory. 

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In set theory, a proper 
subset would be written as: 

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In Python, we use the less than symbol: 

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Birds is a subset of Animals, and we also 
say that Animals is a superset of Birds. 

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That means all the items of 
Birds are contained in Animals. 

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The two terms are complementary. If set A is 
a subset of B, then set B is a superset of A. 

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In set theory, that's written:

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In Python, we use the greater than or equal to symbol:

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Animals is also a proper superset of Birds.

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A proper superset is a set that contains 
another set, but isn't equal to it. 

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In set theory, that's written:

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In Python, we use the greater than symbol:

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With small sets, when we can draw 
diagrams, it's fairly easy to work 

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out if one set is a superset or subset of another.
When we're working with large sets, or have many 

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sets to check, Python can make this much easier.
Make sure you understand what a subset and 

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a superset is, and that you understand 
what proper subsets and supersets are. 

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A proper subset must contain fewer elements 
than its superset, and a proper superset 

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must contain more elements than the subset.
In the next video, we'll write some Python 

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code to check if one set is a subset of another 
set, then we'll look at a practical application. 

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See you in the next video.