65

5

32

18

B1: ({0, 1, 2….(n-1)}, xm), where xn stands for “multiplication-modulo-n”

B2: ({0, 1, 2….n}, xn), where xn stands for “multiplication-modulo-m”

Both B1 and B2 are considered to be

Groups

Semigroups

Subgroups

Associative subgroups

10

42

5

35

Consider the binary operations on X for a, b ∈ X, a*b = a + b + 4. It satisfies the properties of

Abelian group

Semigroup

Multiplicative group

Isomorphic group

Closure property

Identity property

Symmetric property

Associative property

1

56

14

78

A group G, ({0}, +) under addition operation satisfies which of the following properties?

Identity, multiplicity and inverse

Closure, associativity, inverse and identity

Multiplicity, associativity and closure

Inverse and closure

If (M, *) is a cyclic group of order 73, then the number of generators of G is equal to

89

23

72

17

Closure property

Associative property

Symmetric property

Identity property

A trivial subgroup consists of

Identity element

Coset

Inverse element

Ring

The minimum subgroup of a group is called a

Commutative subgroup

Lattice

Trivial group

Monoid

8

2

3

4

__ is not necessarily a group property

Commutativity

Existence of inverse for every element

Existence of Identity

Associativity

A group of rational numbers is an example of a

Subgroup of a group of integers

Subgroup of a group of real numbers

Subgroup of a group of irrational numbers

Subgroup of a group of complex numbers

A relation (34 × 78) × 57 = 57 × (78 × 34) can have the __ property.

Distributive

Associative

Commutative

Closure