Exploring the World of Sets

What is a set? Provide an example.

• [1, 2, 3, 4]

• {1, 2, 3}

• {1, 2, 3, 4}

• An example of a set is {1, 2, 3, 4).

Answer explanation

Brackets and parenthesis are not considered as examples of sets

Identify the elements in the set A = {2, 4, 6, 8}.

• {2, 4, 6, 8}

• {8, 10, 12}

• {2, 4, 6}

• {1, 3, 5, 7}

Answer explanation

Elements are the items inside the set, anything that does not exist inside a set, is not included as one of it's element/s

Is {1, 2} a subset of {1, 2, 3, 4}?

• {1, 2} is a superset of {1, 2, 3, 4}

• Yes

• No

• {1, 2} is equal to {1, 2, 3, 4}

Determine if {3, 4} is a proper subset of {1, 2, 3, 4}.

• {3, 4} is a proper superset of {1, 2, 3, 4}

• Yes

• {3, 4} is a subset of {1, 2, 3, 4}

• {3, 4} is not a subset of {1, 2, 3, 4}

What is the cardinality of the set B = {a, b, c, d, e}?

• 6

• 4

• 5

• 3

Define a null set and provide an example.

• A null set contains at least one element.

• An example of a null set is {1, 2, 3}.

• A null set is a set with infinite elements.

• An example of a null set is ∅ or {}.

What is a universal set? Give an example.

• The set of all even numbers, denoted as E = {2, 4, 6, ...}.

• An example of a universal set is the set of all natural numbers, denoted as N = {0, 1, 2, 3, ...}.

• The set of all integers, denoted as Z = {..., -2, -1, 0, 1, 2, ...}.

• The set of all prime numbers, denoted as P = {2, 3, 5, 7, ...}.

Illustrate a Venn diagram for the sets A = {1, 2, 3} and B = {2, 3, 4}.

• A Venn diagram with two overlapping circles: Circle A contains 1, 2, 3; Circle B contains 2, 3, 4; Intersection contains 2, 3.

• A Venn diagram where Circle A contains only 1 and Circle B contains only 4.

• A Venn diagram with separate circles for A and B without overlap.

• A Venn diagram with one circle containing all elements.

How many elements are in the null set?

• -1

• 0

• 5

• 1

If C = {x | x is an even number}, what is a possible element of C?

• 5

• 7

• 3

• 2