Homework Statement
Prove, that a senigruop S is a group if and only if for every x in S there exists a unique x' in S so that xx'x=x.
Homework Equations
The Attempt at a Solution
I am trying to prove that xx'=1S for all x in S. But all I can show is that xx' is in ES={x | x^2=x}...
Homework Statement
Either A or B (names changed) stole the exam answers. Formalize these and check if this is a correct deduction:
1) If A didn't meet B for lunch, then B is guilty or A lives in the countryside
2) If B isn't guilty, then A didn't meet B for lunch and the incident happened...
Can you help me with this problem:
if a^2 divides b^2, show that a divides b.
This was a homework question that I had a while ago and it was solved by using the fundamental theorem of arithmetic.
I instead tried to solve it with proof by contradiction:
a^2 divides b^2 implies a divides...