Question

Tour answer.
. S. T. the set of all non-negative integers is not a group under
addition,
s. T. the set of all non zero real numbers is a Abelian
group under multiplication.
S. T. the set 0 of all rational numbers is not a group under
multiplication.​

Answer 1

Answer:

The non-zero integers under multiplication has an identity element 1.However, not every integer has a multiplicative inverse.So this does not have multiplicative inverse.Hence it is not a group.

The set of integers is a group under the OPERATION of addition:The integers under the OPERATION of addition are CLOSED, ASSOCIATIVE, have IDENTITY 0, and that any integer x has the INVERSE −x. Because the set of integers under addition satisfies all four group PROPERTIES, it is a group

The set of real numbers is a group with respect to addition as the group is isomorphic to the set of real numbers without 0 with respect to multiplication. What's more is that this group is abelian, that means any two elements will commute with respect to addition.

A group is a set equipped with a binary operation that combines any two elements to form a third element in such a way that four conditions called group axioms are satisfied, namely closure, associativity, identity and invertibility. Only option A does not satisfy this definition. Hence, option (A) is not a Group.