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Set Theory Basics: Empty Set and Universe

17 Questions

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Set Theory Basics: Empty Set and Universe

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Questions and Answers

If x ∈ C, what does that imply according to the text?

x is in set A only

x is not in set A or B

x is in set B only

x is in set A and B (correct)

What does it mean when two sets A and B are disjoint?

A ∩ B is the empty set (correct)

A and B are subsets of each other

A and B have elements in common

A ∪ B includes all elements of A and B

If A = {1, 2, 3} and B = {2, 3, 4}, what is A ∩ B?

{2, 3} (correct)

{2, 3, 4}

{}

{1, 2, 3, 4}

In the context of sets, what does x ∈ C mean?

x is an element common to A and B Signup and view all the answers

If A = {1, 2, 3} and B = {4, 5, 6}, what is A ∪ B?

{1, 2, 3, 4, 5, 6} Signup and view all the answers

Which of the following best defines a set?

A collection of elements Signup and view all the answers

If set A = {1, 2, 3}, what type of set is A?

Countable Signup and view all the answers

What kind of function is used to show that a set is countable?

One-to-one and onto function Signup and view all the answers

If set A = {0, 2, 4, 6, 8, ...}, what term best describes it?

Countable Signup and view all the answers

What is the universal set in set theory notation often represented as?

[0, 1] Signup and view all the answers

Which term describes a set that contains no elements?

Empty set Signup and view all the answers

In set theory, what does the symbol ϕ represent?

The empty set Signup and view all the answers

If A = {1, 2, 3, 4, 5, 6, 7, 8}, which of the following is true?

{1, 2, 3} is a subset of A Signup and view all the answers

What does it mean if a set A is said to be not equal to {1, 2, 3}?

Set A contains elements other than {1, 2, 3} Signup and view all the answers

Which of the following statements about the union of sets A and B is correct?

(A ∪ B) contains elements exclusive to either set A or set B Signup and view all the answers

If a ∈ B implies a ∈ A, what can we conclude?

Set B is a subset of set A Signup and view all the answers

What does x ∈ C represent in the context of set theory?

{x} is an element of set C Signup and view all the answers