Which of the following is TRUE ?
A.  Set of all rational negative numbers forms a group under multiplication 
B.  Set of all nonsingular matrices forms a group under multiplication 
C.  Set of all matrices forms a group under multipication 
D.  Both (b) and (c) 
Option: B Explanation : Click on Discuss to view users comments. 
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 : Click on Discuss to view users comments. 
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)
Click on Discuss to view users comments. waqas said: (10:35pm on Thursday 26th September 2013)
in option C the statement shoud be The set of non zero rational numbers forms an abelian group under multiplication
Vinodh Routhu said: (7:14pm on Sunday 24th August 2014)
the set of rational numbers satisfy abelian group under addition and multiplication

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 : Click on Discuss to view users comments. 