Here we are proving another theorem within set theory. This theorem is covered in "A Transition to Advanced Mathematics," by Smith, Eggen, and St. Andre.
Couldn't we do it using Venns diagram? Where the A and B cricle intersect it denominates the union of two groups. In that case , some of the A's values are withing the unions intersection which would automatically make A a subgroup of A U O, correct me if I'm wrong or if theres a flaw in my logic.
@missemotional8710 Venn Diagrama and pictures are great to help aid in understanding and visualizing a proof. However, pictures can not be the entire proof.
Brain is a bit wine-addled atm, but off-the-cuff I like the following: if x not in A and x not in B then x not in A since this above contrapositive is trivially true, then the statement is true
Please Clear me one thing... Clearly,x is an element of A then Why you are using x might be an element on B(I mean x also belongs to B) ...Why?
The line "x in A implies x in A or x in B?"
@@snellbrosmath yeah
Well, T=T or F. Also, T=T or T. So regardless of if "x in B" is true or false, if "x in A" is true, then "x in A or x in B" is true.
why can't you just write one line and say "that is the definition of what U is"
Can you give me a sample argument?
Because that’s hand waving and this appears to be introductory set theory where many students learn rigorous proofs for the first time.
Couldn't we do it using Venns diagram? Where the A and B cricle intersect it denominates the union of two groups. In that case , some of the A's values are withing the unions intersection which would automatically make A a subgroup of A U O, correct me if I'm wrong or if theres a flaw in my logic.
@missemotional8710 Venn Diagrama and pictures are great to help aid in understanding and visualizing a proof. However, pictures can not be the entire proof.
Brain is a bit wine-addled atm, but off-the-cuff I like the following:
if x not in A and x not in B then x not in A
since this above contrapositive is trivially true, then the statement is true
i think the original proposition is just as trivial lol
@jordancaasi5361 for sure - am just a big fan of the contrapositive haha