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.
Пікірлер: 12
@saravana42174 ай бұрын
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?
@snellbrosmath4 ай бұрын
The line "x in A implies x in A or x in B?"
@saravana42174 ай бұрын
@@snellbrosmath yeah
@snellbrosmath4 ай бұрын
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.
@firstname43378 ай бұрын
why can't you just write one line and say "that is the definition of what U is"
@snellbrosmath8 ай бұрын
Can you give me a sample argument?
@TheSeriousSean8 ай бұрын
Because that’s hand waving and this appears to be introductory set theory where many students learn rigorous proofs for the first time.
@missemotional87108 ай бұрын
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.
@snellbrosmath8 ай бұрын
@missemotional8710 Venn Diagrama and pictures are great to help aid in understanding and visualizing a proof. However, pictures can not be the entire proof.
@roflattheworld8 ай бұрын
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
@jordancaasi53618 ай бұрын
i think the original proposition is just as trivial lol
@roflattheworld8 ай бұрын
@jordancaasi5361 for sure - am just a big fan of the contrapositive haha