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61. Which of the following statements is FALSE ?

The set of rational numbers is an abelian group under addition

The set of rational integers is an abelian group under addition

The set of rational numbers form an abelian group under multiplication

None of these

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

6

8

4

2

63. Match the followingA. Groups I. AssociativityB. Semi groups II. IdentityC. Monoids III. Commutative D. Abelian Groups IV Left inverseCodes. A B C D

IV I II III

III I IV II

II III I IV

I II III IV

64. Let (Z, *) be an algebraic structure, where Z is the set of integers and the operation * is defined by n * m = maximum (n, m). Which of the following statements is TRUE for (Z, *) ?

(Z, *) is a monoid

(Z, *) is an abelian group

(Z, *) is a group

65. Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G ?

g = g^{-1} for every g ∈ G

g = g^{2} for every g ∈ G

(g o h) ^{2} = g^{2}o h^{2 }for every g,h ∈ G

G is of finite order

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