Set Definitions

Question 1

What is a SET?

Answer 1

A set is a collection of Objects

Question 2

Does Order and Repetition in a set matter? Yes or No?

Answer 2

NO it does not matter in a set

Question 3

Is Ø (empty) a ⊆ (subset) of {1,2,3}?

Answer 3

Yes its a set within a set even if it is empty its still a set!

Question 4

What is the Cartesian product definition?

Answer 4

The Cartesian product A x B is the set of all ordered pairs (a,b) where a ∈ A and b ∈ B.

Question 5

Deft: Two sets are Equal

Answer 5

Two sets are equal if and only if they have the same elements. Therefore, if A and B are sets, then A and B are equal if and only if ∀𝑥(𝑥 ∈ 𝐴 ↔ 𝑥 ∈ 𝐵).We write A = B if A and B are equal sets.

Question 6

Deft: Subset

Answer 6

The set A is a subset of B if and only if every element of A is also an element of B.We use the notation A ⊆ B to indicate that A is a subset of the set B.

Question 7

Deft: Let S be a Set

Answer 7

If there are exactly n distinct elements in S where n is a nonnegative integer, we say that S is a finite set and that n is the cardinality of S. The cardinality of S is denoted by |S|.

Question 8

Deft: Infinite set

Answer 8

A set is said to be infinite if it is not finite.

Question 9

Deft: Given a set S

Answer 9

Given a set S, the power set of S is the set of all subsets of the set S. The power set of S is denoted by 𝑃(𝑆).

Question 10

Deft: Let A and B be sets. Union

Answer 10

The union of the sets A and B, denoted by A ∪ B, is the set that contains those elements that are either in A or in B, or in both.

Question 11

Deft: Let A and B be sets. Intersection

Answer 11

Let A and B be sets. The intersection of the sets A and B, denoted by A ∩ B, is the set containing those elements in both A and B.

Question 12

Deft: Venn Diagram - Empty set

Answer 12

Two sets are called disjoint if their intersection is the empty set.

Question 13

Deft: Let A and B be sets. Difference A - B

Answer 13

Let A and B be sets. The difference of A and B, denoted by A − B, is the set containing those elements that are in A but not in B. The difference of A and B is also called the complement of B with respect to A.

Question 14

Deft: Complement A

Answer 14

Let U be the universal set. The complement of the set A, denoted by 𝐴̅ is the complement of A with respect to U. Therefore, the complement of the set A is U − A.

Question 15

Deft: Union collection of a Set

Answer 15

The union of a collection of sets is the set that contains those elements that are members of at least one set in the collection.

Question 16

Deft: The Intersection of a collection of a set

Answer 16

The intersection of a collection of sets is the set that contains those elements that are members of all the sets in the collection.