Sets and Set Notation

Question 1

Define the meaning of the word “set”.

Answer 1

A set is a well-defined collection of distinct items or objects.

Question 2

Which of the following is a set?

1. Collection of animals weighing at least 300 kg
2. Collection of large animals

Answer 2

1

Question 3

Which of the following is a set?

1. Collection of rich people
2. Collection of billionaires

Answer 3

2

Question 4

What are the objects or items in the set called?

Answer 4

elements

Question 5

What does “…” mean and when do you use it?

Answer 5

It is an ellipsis. There are two uses, one is to indicate infinity, the other is to save writing long lists.

Question 6

What does “∈” mean?

Answer 6

It means that an object is an element of the set.

Question 7

What does “∉” mean?

Answer 7

It means that the term is not an element of the set.

Question 8

Given set Y= {1, 3, 5, …, 55, 57, 59}

20∈/∉ Y

Answer 8

∉

Question 9

Define what A⊆B means.

Answer 9

It means that set A is a subset of set B because all the elements of set A are in set B.

Question 10

Define what A⊂B means.

Answer 10

It means that set A is a proper subset of B because set A is a subset of set B and B has at least 1 element that is not in A.

Question 11

What is the formula to get the number of subsets in a set?

Answer 11

2^n

Question 12

What is the formula to get the number of proper subsets in a set?

Answer 12

2^n-1

Question 13

What is a universal set?

Answer 13

Denoted by U, is the set of all possible elements of any set used in the problem.

Question 14

Define an empty set or null set.

Answer 14

It is a set with no elements.

Question 15

True or False.

An empty set is always a subset of any set.

Answer 15

True

Question 16

Differentiate equal sets from equivalent sets.

Answer 16

Equal sets are sets that contain exactly the same elements while equivalent sets are sets that contain exactly the same number of elements.

Question 17

What is the sign for equivalent sets?

Answer 17

≈

Question 18

Can a set contain repeated elements?

Answer 18

No.

Question 19

Differentiate finite sets from infinite sets.

Answer 19

A finite sets is one in which it is possible to count all the elements of the set. An infinite set is one in which it is not possible to list and count all the elements of the set.

Question 20

What is the symbol for cardinality?

Answer 20

I I

Question 21

What is a verbal description?

Answer 21

Describing a set in words

Question 22

What is the roster/tabular method?

Answer 22

Listing each element of the set inside braces

Question 23

What is the rule method/set builder notation?

Answer 23

Listing the rules that determine whether an object is an element of the set rather than actual elements

Question 24

How do you read xIx?

Answer 24

X such that x