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 :

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zuhaib said: (3:10pm on Friday 24th February 2017)
multiplication identity is '1' and additive edentity is '0'..thats right answer is '0' has no invers
Kith said: (2:23pm on Wednesday 22nd March 2017)
R-{0} is a group under multiplication

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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:  

image 113. 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 :

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4:  

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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5:  

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

A.

1

B.

-1

C.

i

D.

-i

 
 

Option: C

Explanation :

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Amit kumar said: (5:57pm on Sunday 26th November 2017)
As we know a.a^-1 =a^-1.a = e And 1 is the multiplicative identity element As (i ×-i )=1So i is the inverse element of i

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