# Set Theory and Algebra MCQ - Sets

36:

Which of the following is TRUE ?

 A. Set of all rational negative numbers forms a group under multiplication B. Set of all non-singular matrices forms a group under multiplication C. Set of all matrices forms a group under multipication D. Both (b) and (c) Answer Report Discuss Option: B Explanation : Click on Discuss to view users comments. Write your comments here:
37:

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 Answer Report Discuss Option: D Explanation : Click on Discuss to view users comments. Write your comments here:
38:

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 Answer Report Discuss 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 Write your comments here:
39:

In the group G = {2, 4, 6, 8) under multiplication modulo 10, the identity element is

 A. 6 B. 8 C. 4 D. 2 Answer Report Discuss Option: A Explanation : Click on Discuss to view users comments. Write your comments here:
40:

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 Answer Report Discuss Option: A Explanation : Click on Discuss to view users comments. Write your comments here: