Week 2

Question 1

What is a set?

Answer 1

A set is a collection of unique elements.

Question 2

What does |S| mean?

Answer 2

|S| = the size of set S = the number of unique elements in S
|S| = can be infinite such as the set of real numbers or rational numbers

Question 3

What is the definition of a subset?

Answer 3

A is a subset of B if all the elements in A are also in B.

Question 4

What does it mean if two sets are equal?

Answer 4

Set A is equal to Set B if they both have exactly the same elements.

Question 5

How can you prove that two sets are equal?

Answer 5

Prove that A is a subset of B and B is a subset of A.

Question 6

Define the following: A union B

Answer 6

A union B is a set that contains all the elements in A and B stitched together.

Question 7

Define the following: A intersect B

Answer 7

A intersect B is a set that contains all the elements that appear in both A and B.

Question 8

Define the following: A subtract B

Answer 8

A difference B is a set that contains all the elements in A without the elements that also appear in B.

Question 9

What do the following set definitions mean?
{ x | x e A or x e B}
{ x | x e A and x e B}

Answer 9

A union B
A intersect B

Question 10

What is the empty set?

Answer 10

A set that contains no elements

Question 11

Is the empty set a subset of all sets?

Answer 11

Yes