
Exploring Advanced Algebra Concepts
Quiz
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Mathematics
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Professional Development
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Practice Problem
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Hard
mahinder singh
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23 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the set of integers and how is it represented in algebra?
The set of integers is represented as R = {..., -2.5, -1.5, 0, 1.5, 2.5, ...}.
The set of integers includes only positive numbers.
The set of integers is represented as I = {0, 1, 2, 3}.
The set of integers is represented as Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Define congruence in algebra and provide an example.
For example, 14 ≡ 2 (mod 12) because both 14 and 2 leave a remainder of 2 when divided by 12.
14 ≡ 3 (mod 12) because both 14 and 3 leave a remainder of 3 when divided by 12.
14 ≡ 0 (mod 12) because both 14 and 0 leave a remainder of 0 when divided by 12.
14 ≡ 5 (mod 10) because both 14 and 5 leave a remainder of 4 when divided by 10.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What are the properties of a group in algebra?
A group has the properties of closure, associativity, identity, and invertibility.
A group is defined by its commutativity property.
A group requires a finite number of elements.
A group must have a maximum element.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Explain the concept of a subgroup and give an example.
The set of all integers under multiplication is a subgroup of the group of all integers under addition.
An example of a subgroup is the set of even integers under addition, which is a subgroup of the group of all integers under addition.
The set of odd integers under multiplication is a subgroup of the group of all integers under addition.
The set of prime numbers under addition is a subgroup of the group of all integers under addition.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a normal group and how does it differ from a regular group?
A normal group is one where all elements commute; a regular group has non-commuting elements.
A normal group is defined by its order; a regular group is defined by its elements.
A normal group has only one subgroup; a regular group has multiple subgroups.
A normal group is one where every subgroup is normal; a regular group has coinciding left and right cosets.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Define a cyclic group and provide an example of one.
The group of rational numbers under multiplication, (Q, ×), is an example of a cyclic group.
The set of all even integers under addition, (2Z, +), is an example of a cyclic group.
The group of integers under addition, (Z, +), is an example of a cyclic group.
The group of non-zero real numbers under addition, (R\{0}, +), is an example of a cyclic group.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the significance of the identity element in a group?
The identity element is crucial as it allows every element in the group to combine with it without changing the element.
The identity element is not necessary for group structure.
The identity element is only relevant in abelian groups.
The identity element can change the outcome of operations.
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