MAT 102
Dropbox Assignment 3: Mathematical Systems
INSTRUCTIONS
- Present your handwritten work neatly for all questions shown below.
- Justify your answers to receive full credit.
Problem 1 [9 pts]
Determine whether the following mathematical systems are groups or
not. If it's a group, explain why all four group conditions (closure,
identity, inverses, associativity) are satisfied. Also, specify if the group
is Abelian (commutative). If it's not a group, show at least one of the
four group conditions that is not satisfied.
a) The set of even integers under addition.
b) The set of positive unit fractions under multiplication.
A unit fraction is any fraction with numerator 1, such as ½ or 1/5.
c) The set of real numbers under the averaging binary operation,
which takes the sum of these numbers and divides it by 2.
