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Fundamentals of Computing

What does commutative mean?

It doesn't matter which way round we write the arguments

Fundamentals of Computing

What does associative mean?

It doesn't matter which way we bracket two union or two intersection operations.

Fundamentals of Computing

What does distributive mean?

The union and intersection operators interact in a specific way.

If there are two sets of brackets that have A Union B and A Union C, connected by an intersection symbol, this can be shortened to A Union (B Intersection C). Vice versa, if there are two sets of brackets that have A intersection B and A intersection C connected by a Union symbol, this can be shortened to A intersection (B union C)

Fundamentals of Computing

What does idempotent mean?

Applying the union or intersection operations to the same set twice has no effect. Useful when cancelling.

Fundamentals of Computing

What is the identity rule?

A Union with an empty set equals A

Fundamentals of Computing

What are the two ways you can define a relation?

1) Property - state the property that defines when the relation is true

2) Subset - define the actual subset of elements the relation is true for

Fundamentals of Computing

What does reflexive mean?

The relation is reflexive is R(x,x) holds for every value of x that is in A

Fundamentals of Computing

What does symmetric mean?

A relation is symmetric if whenever R(x,y) holds, R(y,x) also holds for any x,y in A.

Fundamentals of Computing

What does transitive mean?

A relation is transitive if whenever R(x,y) and R(y,z) hold, R(x,z) also holds for any x,y,z in A.

Fundamentals of Computing

What is a function?

A rule for mapping elements between two sets.

Fundamentals of Computing

What is the domain and how is it denoted?

The domain is the set of input elements X and is denoted dom f.

Fundamentals of Computing

What is the codomain and how is it denoted?

The codomain is the set of output elements Y and is denoted cod f.

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