Set Theory

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If A and B are two sets, then what is A – B equal to?

A ∪ B

A ∪ B'

A ∩ B

A ∩ B' (correct)

For any set A, what is the result of A ∪ A?

A (correct)

U

A ∩ A

A ∪ ∅

Which of the following is true according to De Morgan's law?

(A ∩ B)' = A' ∪ B'

(A ∪ B)' = A' ∪ B'

(A ∪ B)' = A' ∩ B' (correct)

(A ∩ B)' = A' ∪ B'

What is the result of A ∩ U for any set A?

A Signup and view all the answers

If A, B and C are three sets, then A × (B ∪ C) is equal to?

(A × B) ∪ (A × C) Signup and view all the answers

If A and B are two sets, what is the result of A Δ B?

B Δ A Signup and view all the answers

What is the result of A ∩ (B ∪ C) for any three sets A, B, and C?

(A ∪ B) ∩ C Signup and view all the answers

What is A ∩ (B – C) equal to?

(A ∩ B) – (A ∩ C) Signup and view all the answers

If A, B and C are three sets, then (A – B) ∪ (B – A) is equal to?

(A ∪ B) – (A ∩ B) Signup and view all the answers

What is the result of A - (B - C) for any three sets A, B, and C?

(A - C) - B Signup and view all the answers

If A and B are two sets, then what is A – B equal to?

A ∩ Bc Signup and view all the answers

If A, B, and C are any three sets, then A – (B ∪ C) is equal to?

(A – B) ∩ (A – C) Signup and view all the answers

If A and B are two non-empty sets, then what is (A – B) ∪ (B – A) equal to?

(A ∪ B) – (A ∩ B) Signup and view all the answers

Let A and B be two non-empty sets. What is A × B equal to?

{(a, b) : a ∈ A and b ∈ B} Signup and view all the answers

If A and B are two non-empty sets, then what is A – (A ∩ B) equal to?

A – B Signup and view all the answers

Which of the following sets is a null set?

The set {x : x^2 + 1 = 0 and x is real} Signup and view all the answers

If A is a set of integers, what is the set notation for A?

A = {x | x is an integer and x = 2n for n ∈ Z} Signup and view all the answers

What is the set notation for the set of all even natural numbers?

E = {x | x is a natural number and x = 2n for n ∈ N} Signup and view all the answers

Which of the following is a well-defined collection?

The set of all students in a class Signup and view all the answers

What is the set of all real numbers denoted by?

R Signup and view all the answers

What is a common term used to describe the objects that constitute a set?

Elements Signup and view all the answers

What is the purpose of a rule in defining a set?

To tell whether a given object belongs or does not belong to the set Signup and view all the answers

What is the significance of the order in which elements are written in a set?

It makes no difference Signup and view all the answers

What is the symbol used to read as 'such that' in the set-builder method?

| Signup and view all the answers

What is the notation used to describe a set using the roster method?

{ } Signup and view all the answers

What is the total number of subsets of a set A with n elements?

$2^n$ Signup and view all the answers

If a set A has $m$ elements and a set B has $n$ elements, and the total number of subsets of A is 56 more than the total number of subsets of B, what are the values of $m$ and $n$?

m = 6, n = 3 Signup and view all the answers

What is the number of proper subsets of the set {1, 2, 3}?

6 Signup and view all the answers

If X = {8n - 7n - 1 : n ∈ N} and Y = {49(n - 1) : n ∈ N}, then what is the relationship between X and Y?

X ⊆ Y Signup and view all the answers

If A = {x : x ∈ R, x^2 = 16 and 2x = 6}, what is the value of A?

∅ Signup and view all the answers

Set Theory

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Questions and Answers

If A and B are two sets, then what is A – B equal to?

For any set A, what is the result of A ∪ A?

Which of the following is true according to De Morgan's law?

What is the result of A ∩ U for any set A?

If A, B and C are three sets, then A × (B ∪ C) is equal to?

If A and B are two sets, what is the result of A Δ B?

What is the result of A ∩ (B ∪ C) for any three sets A, B, and C?

What is A ∩ (B – C) equal to?

If A, B and C are three sets, then (A – B) ∪ (B – A) is equal to?

What is the result of A - (B - C) for any three sets A, B, and C?

If A and B are two sets, then what is A – B equal to?

If A, B, and C are any three sets, then A – (B ∪ C) is equal to?

If A and B are two non-empty sets, then what is (A – B) ∪ (B – A) equal to?

Let A and B be two non-empty sets. What is A × B equal to?

If A and B are two non-empty sets, then what is A – (A ∩ B) equal to?

Which of the following sets is a null set?

If A is a set of integers, what is the set notation for A?

What is the set notation for the set of all even natural numbers?

Which of the following is a well-defined collection?

What is the set of all real numbers denoted by?

What is a common term used to describe the objects that constitute a set?

What is the purpose of a rule in defining a set?

What is the significance of the order in which elements are written in a set?

What is the symbol used to read as 'such that' in the set-builder method?

What is the notation used to describe a set using the roster method?

What is the total number of subsets of a set A with n elements?

If a set A has $m$ elements and a set B has $n$ elements, and the total number of subsets of A is 56 more than the total number of subsets of B, what are the values of $m$ and $n$?

What is the number of proper subsets of the set {1, 2, 3}?

If X = {8n - 7n - 1 : n ∈ N} and Y = {49(n - 1) : n ∈ N}, then what is the relationship between X and Y?

If A = {x : x ∈ R, x^2 = 16 and 2x = 6}, what is the value of A?

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