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Quiz Questions
Question 1: What is an identity element in a group?
An element that's in every group
The inverse
A random element
An element that leaves all others unchanged
Question 2: Is the set of integers under addition a group?
Undefined
Sometimes
No
Yes
Question 3: What is a subgroup?
A group within a group structure
A subset that is also a group under the same operation
A group with fewer elements
Any subset of a group
Question 4: What is the order of a finite group?
The number of elements in the group
The largest element
The inverse count
The identity count
Question 5: Is the set of real numbers under multiplication a group?
Yes
No (0 has no inverse)
Undefined
Sometimes
Question 6: What is a ring?
A group with two operations
A set of numbers
An algebraic structure with + and · satisfying certain axioms
A multiplication of groups
Question 7: Is Z (integers) a ring under addition and multiplication?
No
Sometimes
Undefined
Yes
Question 8: What property does a commutative group have?
a*a = a
a + b = 0
a*b ≠ b*a
a*b = b*a for all a,b
Question 9: What is the inverse of element a in a group?
The opposite of a
Zero
An element a^(-1) such that a*a^(-1) = e
The negative of a
Question 10: Is the symmetric group S_3 abelian (commutative)?
Yes
Sometimes
No
Undefined
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