Lecture 1

Question 1

What is a set?

Answer 1

An unordered collection of objects with no duplication.

Question 2

What ways can sets be combined?

Answer 2

∪ is called union, meaning the sets combine to form one set which contains all objects from both sets.
∩ is called intersection, this means only objects in both sets make it into the new set
• − is called difference or relative complement, e.g A - X means the final set is A, but with objects shared with X removed.
• if our sets exist in some “universe”, U, (e.g. the integers) then we also have a notion
of complement, where Xc = U − X, so basically the complement set is the set of all things not in the original set.

Question 3

What is a partition

Answer 3

A collection of sets partition a set if the sets collectively make up the bigger set and no items are repeated in between any sets.

Question 4

What is set builder notation?

Answer 4

X = {x|some property that x holds}

Question 5

What is an ordered pair?

Answer 5

two sets combine to form a set where the first item comes from the first set and the second from the second set.

Question 6

What is a relation from sets?

Answer 6

A subset of the two sets times each other. This can be illustrated by drawing arrows from one point to the other.

Question 7

What is a function?

Answer 7

A special sort of relation which has exactly one arrow from each element of the first set. A partial function is similar except that some elements from the first set may not have arrows starting from them.
The set of all functinos from A to B is denoted B^A