Can You Prove a power set problem?

We show that the difference of A and B is an element of the power set of A using a formal proof. This would be covered in set theory in discrete mathematics.
#SetTheory #DiscreteMath #SetProof
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[@Loki-]

I really needed more Discrete math! I'm out of university, but I need to refresh on this to get back into algorithms/data structures.
Also, thank you for fixing the audio! It sounds perfect now!

[@yamatanoorochi3149]

A−B⇔(x ∈ A)∧(x ∉ B)
⇔x ∈ A
∴ (A−B) ⊆ A
And powersets are the family of subsets in A
∴ (A−B) ∈ P(A)
That's how I did it 🤔 I don't know if I made any technical mistakes or jumped to conclusions that needed more proof

[@dramapro2322]

Thanks

[@Michelle-ep3gg]

Isn't the power set by definition "the set that contains all subsets of a given set" therefore A-(literally anything) will always be a subset of P(A). Am I missing something? Can I use the definition as the proof?

[@minh355]

Okay correct me if I am wrong but I think this is another way to solve this problem using the rules of power sets. Could you just prove that (A-B) is a subset of (A), then you could use the rules to turn (A-B) is subset of (A) into (A-B) is element of Superset(A)?

[@Trevtutor]

Yep that’s another way that works. This method just gets a little more conceptual teaching in it to extend to other problems.

[@philosophyversuslogic]

Sorry, but P(A-B)cP(A) cannot be proved verbally only. And this is why I don't get along with the set theory, since it doesn't supply us with the formal proofs. Despite the fact, I understand P(A-B)cP(A) without formal proof.