Question

Let A be the set of all odd integers. The set A with respect to multiplication is

• A. a monoid but not group
• B. a semi group but not a monoid
• C. not a semi group
• D. a group

Answer 1

The correct option is A a monoid but not group

option (b)

Product of any two odd intergers is also an odd integer.

Therefore, A is closed with respect to multiplication.

Multiplication of integers is associative.

1 is identity element

The inverse of an odd integer with respective multiplication need not be an odd integer.

Ex: Inverse of 3 is
$\frac{1}{3}$

$\therefore$ A is a monoid with respective multiplication but not a group.