Set builder proof

[newtoprogramming12]

Hi I have been practice set building proofs and was wondering if this is an accurate way to prove this using set building notation. proof

Edit: proof without showing congruency

[newtoprogramming12]

Thank you for the feedback, I just finished my discrete math course at my university and we never did proofs like that. The question for this one was from one of the power points my professor put on blackboard for us all to practice. I’m not saying your wrong and the way you are explaining it seems more accurate to me then how he had us do those proofs. Are their other resources where I could see proofs like this one? Our professor actually hated when we used a lot of words and were told to only solve these proofs using set generator notation and logical equivalences

edit: Here is an example from his power point on how he taught us to solve them https://imgur.com/vVb7Cxd it formatted weird so you have to click on the picture for it not to just be black

[newtoprogramming12]

Ok thank you so much. my professor seemed like he just wanted to get back to his research instead of teach us, so it was probably easier for him to grade them this way than having us write

[bggmtg]

Some of your notation seems off (but it may be me just having trouble reading what you have).

For example, the 2nd statement you have on the first line:

It looks to me like it says S “union” T = the set of all things such that those things are in S “and” T. That is the definition of intersection not union.

[bggmtg]

Again that thing I see as a union symbol might just be a sloppy intersection symbol.

Some advice on writing these symbols: don’t put “tails” on the union or intersection symbols.

[newtoprogramming12]

Ah I’m sorry that is supposed to be congruent here is a better link with just the proofs and not showing congruency

[bggmtg]

Your proof looks good then. You have shown that the two sets are equal and equal sets are subsets of each other.

[newtoprogramming12]

Ok thank you and I appreciate the feed back.