Classical

Set Theory and Algebra MCQ - Sets

21:  

 If f : A ---> B is a bijective function, then f -1 of f =

A.

f o f -1

B.

f

C.

f -1

D.

IA(Identity map of the set A)

 
 

Option: D

Explanation :


22:  

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 :


23:  

If (G, .) is a group such that (ab)- 1 = b-1 a-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 :


24:  

If * is defined on R* as a * b = (ab/2) then identity element in the group (R*, *) is

A.

1

B.

2

C.

1/2

D.

1/3

 
 

Option: B

Explanation :


25:  

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 :




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