Today, we’re going to explore the concept of sets. Can anyone tell me what a set is?

Exactly! A set is a well-defined collection of distinct objects called elements. Think of it as a way to group things together. For example, {1, 2, 3} is a set of numbers. Remember, we can think of sets using the acronym **S-E-E**: Set, Elements, and Everything well-defined.

Great question! We have finite sets, infinite sets, empty sets, and more. A finite set has a limited number of elements, while an infinite set continues forever. Let's remember these with the mnemonic **F-I-E**: Finite, Infinite, Empty.

The empty set contains no elements and is denoted by {} or ∅. It’s a crucial concept since it serves as a basis for understanding sets. Let’s recap: sets group distinct items, and we have different types like finite, infinite, and empty.

Now that we know about sets, let’s look at some basic operations performed on them. Can anyone name an operation on sets?

Yes! The **union** of two sets combines all unique elements from both. It’s denoted by the symbol ∪. A memory aid to remember this is **U for Uniting**. What about other operations?

Exactly! The **intersection** finds common elements between two sets, denoted by ∩. To remember, think of **I for In and Common**. Let’s also not forget the properties of these operations.

We have properties like commutative, associative, and distributive laws, as well as De Morgan's laws. It’s essential to know these rules to manipulate sets effectively. Recap: we unite sets with union, find common ground with intersection, and follow properties for operations.

Let’s shift our focus to functions. What can you tell me about them?

Correct! A function assigns exactly one output in the co-domain for each input from the domain. To remember this, think **F for Function, One Output**. What are the three main parts of a function?

Well done! The domain is all possible inputs, the co-domain is the set of potential outputs, and the range is the actual outputs. Let’s remember with **D-C-R**: Domain, Co-domain, Range. It’s vital to distinguish these components when working with functions.

Now let’s move on to types of functions. Who can name a type?

Yes! An injective function maps each input to a unique output. There’s also the surjective function, which maps to every element in the co-domain. Let’s remember them with the phrase **I-S-B**: Injective, Surjective, Bijective. What do you think bijective means?

Exactly! Bijective functions have a perfect pairing between domain and co-domain elements. Also, we have constant functions, where the output remains the same. Let’s recap: we discussed injective, surjective, and bijective functions.