Classical

Set Theory and Algebra MCQ - Algebra

1:  

The set of all real numbers under the usual multiplication operation is not a group since

A.

multiplication is not a binary operation

B.

multiplication is not associative

C.

identity element does not exist

D.

zero has no inverse

 
 

Option: D

Explanation :


2:  

If (G, .) is a group such that (ab)- 1 = a-1b-1, ∀ a, b ∈ G, then G is a/an

A.

commutative semi group

B.

abelian group

C.

non-abelian group

D.

None of these

 
 

Option: B

Explanation :

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3:  

If (G, .) is a group such that a2 = e,  ∀a ∈ G, then G is

A.

semi group

B.

abelian group

C.

non-abelian group

D.

none of these

 
 

Option: B

Explanation :


4:  

The inverse of - i in the multiplicative group, {1, - 1, i , - i} is

A.

1

B.

-1

C.

i

D.

-i

 
 

Option: C

Explanation :


5:  

The set of integers Z with the binary operation "*" defined as a*b =a +b+ 1 for a, b ∈ Z, is a group. The identity element of this group is

A.

0

B.

1

C.

-1

D.

12

 
 

Option: C

Explanation :




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