well-defined collection of objects

the description method is used, and it is more convenient

the description method is not used

the description method is never used

Set Theory And Logic Quiz

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Talanti

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1/10 Questions

A set is:
- Collection of objects
- Well-defined collection of objects
- Elements of the set
- Description
- Collection

About This Quiz

Do you understand the concept of logic and set theory? Take this set theory quiz, and see how well you understand this concept. The process of derivation of properties is called logic. The general properties of sets and elements are called the set theory. Here, we have logic and set theory questions and answers to test your knowledge. All the See morebest! You can share the quiz with others interested in solving math problems.

2.

The symbol ∈ means:
- Is not an element of
- Is description
- Is an element of
- Does not belong
Correct Answer

A. Is an element of

Explanation

The symbol "∈" is used in set theory to indicate that an element belongs to a set. It represents the concept of membership, indicating that the element is part of the set.

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5
3.

For larger sets:
- The description method is used, and it is more convenient
- The description method is not used
- The description method is never used
- All of the above
Correct Answer

A. The description method is used, and it is more convenient

Explanation

The correct answer is "the description method is used, and it is more convenient." This means that for larger sets, the description method is utilized because it is considered to be more convenient. This suggests that the description method is preferred and offers advantages over other methods when dealing with larger sets.

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7
4.

Z = {. . . ,−2,−1, 0, 1, 2, . . .} is the set of integers.
- True
- False
Correct Answer

A. True

Explanation

The statement is true because the set Z includes all integers, which are whole numbers both positive and negative, as well as zero. It is represented by the ellipsis notation, which indicates that the set continues indefinitely in both the negative and positive directions. Therefore, the given statement accurately describes the set of integers.

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6
5.

N = {0, 1, 2, 3, . . .} is the set of integers.
- True
- False
Correct Answer

A. False
6.

All elements of all the sets under discussion belong to some universal set or universe.
- True
- False
Correct Answer

A. True

Explanation

This statement is true because in set theory, all sets are considered to be subsets of a universal set. The universal set contains all the elements that are being discussed in the context of the sets. Therefore, all elements of all the sets under discussion do indeed belong to some universal set.

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12
7.

The empty set is the set containing no elements.
- True
- False
Correct Answer

A. True

Explanation

The empty set, also known as the null set, is a set that does not contain any elements. It is denoted by the symbol Ø or {} and is considered a subset of every set. Therefore, the statement "The empty set is the set containing no elements" is true.

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7
8.

Let A and B be sets. A equals B, written A=B, iff every element of A is also an element of B, and conversely, every element of B is also an element of A.
- True
- False
Correct Answer

A. True

Explanation

The statement is true because it accurately defines the concept of set equality. According to the definition, two sets A and B are equal if and only if every element in A is also in B, and vice versa. This means that if A equals B, then any element that belongs to A must also belong to B, and any element that belongs to B must also belong to A. Therefore, the correct answer is true.

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6
9.

Theorem. There is only one empty set, i.e., only two empty sets are equal.
- True
- False
Correct Answer

A. True

Explanation

This statement is true because the empty set is a unique set with no elements. It is defined as a set that contains no elements, and by definition, there can only be one set that meets this criteria. Therefore, there is only one empty set and any other set that is empty is equal to it.

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9
10.

Let A and B be sets. Then A=B iff A belongs to B.
- True
- False
Correct Answer

A. False

Explanation

The statement "A=B iff A belongs to B" is not entirely accurate. The symbol "iff" stands for "if and only if," which implies a bidirectional or equivalence relationship. In set theory, "A=B" means that sets A and B have the same elements, but it doesn't imply that A belongs to B or vice versa.

If A belongs to B, it would mean that A is an element of B, not that A is equal to B. Likewise, if A is equal to B, it means that A and B have the same elements, but it doesn't necessarily mean that A is an element of B. Therefore, the statement "A=B iff A belongs to B" is not true in general for sets.

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10

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Sep 01, 2024

Quiz Edited by
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Sep 01, 2011

Quiz Created by
Talanti

Set Theory And Logic Quiz

A set is:

Quiz Preview

The symbol ∈ means:

For larger sets:

Z = {. . . ,−2,−1, 0, 1, 2, . . .} is the set of integers.

N = {0, 1, 2, 3, . . .} is the set of integers.

All elements of all the sets under discussion belong to some universal set or universe.

The empty set is the set containing no elements.

Let A and B be sets. A equals B, written A=B, iff every element of A is also an element of B, and conversely, every element of B is also an element of A.

Theorem. There is only one empty set, i.e., only two empty sets are equal.

Let A and B be sets. Then A=B iff A belongs to B.