Question

The set of positive even integers, with usual addition forms

• A. A finite group
• B. Only a semi group
• C. Only a monoid
• D. An infinite group

Answer 1

The correct option is B Only a semi group

Consider a set of positive even integers. The set satisfies following conditions

Closure $($If $a$ belongs to set and $b$ belongs to set then $a+b$ belongs to set$)$
Assosiative $($If $a$ belongs to set and $b$ belongs to set then $a+b=b+a)$
Therefore the set of positive integers, with usual addition forms a semi group
Therefore the correct option is $B$