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Set Theory and Algebra MCQ - Algebra

16:  

 Which of the following statements is FALSE ?

A.

The set of rational numbers is an abelian group under addition

B.

The set of rational integers is an abelian group under addition

C.

The set of rational numbers form an abelian group under multiplication

D.

None of these

 
 

Option: C

Explanation :

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17:  

In the group G = {2, 4, 6, 8) under multiplication modulo 10, the identity element is

A.

6

B.

8

C.

4

D.

2

 
 

Option: A

Explanation :

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18:  

Match the following

A. Groups                         I. Associativity

B. Semi groups              II. Identity

C. Monoids                     III. Commutative
 
D. Abelian Groups         IV Left inverse

Codes. A B C D

A.

IV   I    II   III

B.

III    I   IV   II

C.

II   III   I   IV

D.

I    II    III   IV

 
 

Option: A

Explanation :

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19:  

Let (Z, *) be an algebraic structure, where Z is the set of integers and the operation * is defined by n * m = maximum (n, m). Which of the following statements is TRUE for (Z, *) ?

A.

(Z, *) is a monoid

B.

(Z, *) is an abelian group

C.

(Z, *) is a group

D.

None of these

 
 

Option: D

Explanation :

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20:  

 Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G ?

A.

g = g-1 for every g ∈ G

B.

g = g2 for every g ∈ G

C.

(g o h) 2 = g2o h2 for every g,h ∈ G

D.

G is of finite order

 
 

Option: C

Explanation :

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