ABSTRACT ALGEBRA TEST
Quiz
•
Mathematics
•
University
•
Practice Problem
•
Easy
Judith Aleguen
Used 2+ times
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40 questions
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1.
MULTIPLE CHOICE QUESTION
5 mins • 2 pts
Let a binary operation ‘*’ be defined on a set A. The operation will be commutative if ________
a*b=b*a
(b ο c)*a=(b*a) ο (c*a)
(a*b)*c=a*(b*c)
a*b=a
2.
MULTIPLE CHOICE QUESTION
5 mins • 2 pts
Let be a binary operation on N defined by ab=a-b+ab2, then find 4*5.
9
98
88
99
3.
MULTIPLE CHOICE QUESTION
5 mins • 2 pts
Let ‘&’ be a binary operation defined on the set N. Which of the following definitions is commutative but not associative?
a & b=a-b
a & b=ab – 8
a & b=a+b
a & b=ab
4.
MULTIPLE CHOICE QUESTION
5 mins • 2 pts
Let ‘*’ be a binary operation defined by a*b=4ab. Find (a*b)*a.
4a2 b
16ab2
16a2 b
4ab2
5.
MULTIPLE CHOICE QUESTION
5 mins • 2 pts
Consider the binary operations on X, a*b = a+b+4, for a, b ∈ X. It satisfies the properties of _______.
NOT A GROUP
ABELIAN GROUP
GROUP
6.
MULTIPLE CHOICE QUESTION
5 mins • 2 pts
In a group there must be only __________ identity element.
1
2
3
5
7.
MULTIPLE CHOICE QUESTION
5 mins • 2 pts
Which of the following multiplication tables defined on the set G={a,b,c,d} form a group?
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