Classical

Set Theory and Algebra MCQ - Sets

36:  

The set of all nth roots of unity under multiplication of complex numbers form a/an

A.

semi group with identity

B.

commutative semigroups with identity

C.

group

D.

abelian group

 
 

Option: D

Explanation :


37:  

 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: D

Explanation :

Set of rational numbers  form an abelian group under multiplication .  It satisfies with 0 also.  As we know abelian group follow some properties:
1. associative i.e. ao(boc)= (aob)oc  for 0   0*(1*2)=0 and (0*1)*2=0 so this property has prove 
2. If an element 4 belongs to  G  such that 0o4=0 for all 0 belongs to G 
3. For any a belongs to G and  b belongs to G such that aob=e     for ex:      a=0 b=2  For * 0*2=0  and  0 is identity(e) for multiplication
4. For commutative property 0*4=4*0=0
So all properties of abelian group are followed by  0 also  so  statement is correct
So answer is (D)


38:  

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 :


39:  

 Match the following

A. Groups                     I. Associativity
B. Semi groups          II. Identity
C. Monoids                  III. Commutative
D. Abelian Groups     IV Left inverse

 

A.

A  B  C  D
IV  I   II   III

B.

A  B  C  D
III  I   IV   II

C.

A  B  C  D
II   III  I   IV

D.

A  B  C  D
I    II  III  IV
 

 
 

Option: A

Explanation :


40:  

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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