Proving Set Equality: From Sets to Logic and Back

We work through an example of proving that two sets are equal by proving that any element of one must also be an element of the other. We convert the set claims to logic claims, reason using the standard definitions and identities of Boolean logic, and then convert the final claims back to claims about sets.

We have three videos that illustrate proofs of claims about sets. This is the second one. The first is:

The third is:

[mtdrei]

This made writing proofs in general so much clearer for me. Thank you.

[gorkemyigit]

Wow, I was desperately looking for something like this. I was struggling with a question for a few hours now and solved It in 5 mins after watching this video. Thank you so much.

[lahiruudayanga]

Thanks a lot.I was looking everywhere for a proper explanation and was unable to find a one.But after I watched this all the doubts became clear and the section is totally understandable now.Thanks a lot again

[davidwright]

Many thanks for all three videos. They're very clear. What really helped was the distinction you made between statements in the 'language' of sets and their equivalent in the 'language' of Boolean logic. In which language you can systematically transform statements about sets, then translate the last line in your logical derivation back into set statements directly. Those two levels - set and logic - were muddled in my head. No more!

[muhammadmudassir]

Empty set does not satisfied the definition of set (collection of well define and distinct object) there is no object in empty set but way it's a set... please help me