2 Determine if each of the following is a group a monoid

Last updated: 12/4/2023

2 Determine if each of the following is a group a monoid that is not a group a semigroup that is not a monoid or not a semigroup Explain your answer for each one Z addition on the set of positive integers It farms bernise a group It satisfies closure associativity identity element and every element has an inverse ii Q subtraction on the set of rational numbers This is not a semigroup because the set of rational numbers under subtration isn t closed under subtraction iii C32 addition on a 32 hour clock It satisfies Closure associativity identity element and every element has an in verse It forms a group iv C15 0 multiplication on a 15 hour clock with 0 removed This doesn t form a group or monoid Not element has an inverse every v 0 0 1 0 1 U the set is P 0 1 and the operation is union a semigroup but not a monoid This is on the power set of 0 1 forms a sem igroup The set is closed under the union operation which is associative It doesn t have an identity element so it s not a mencid vi 0 1 2 where x y y for example 0 2 2