# Natural deduction sets (Rules of nature deduction)

Tags:
1. Oct 17, 2014

### emanoelvianna

Hello fine.

I'm studying logic and great difficulties to understand its principles, and should prove some theories involving the laws of identity of sets of mathematics using the method of natural deduction, they are:

a) A ∪ ∅ = A
b) A ∩ ∅ = ∅

I am trying as follows, but I can not solve

http://www.imagesup.net/dm-1514135726215.png [Broken]

Could anyone help me solve ?!
If I could be pointed out to me some book or website to get more doubts which were to appear on deduction of sets I'd appreciate it.
Thank you.

Last edited by a moderator: May 7, 2017
2. Oct 17, 2014

### mathman

I am not sure what you are trying to do, but the basic logic is that the empty set has no elements, so if it is the union it must be in A.

3. Oct 17, 2014

### emanoelvianna

Hello, thank you by return.

I understand the theory that a set, but I need to prove it by natural deduction, this theory is known as "Natural deduction rules for theory set"

The usual way to do proofs about set theory identities is to use logic that involves quantifiers, such as "for each" and "there exists". ( symbolized by $\forall$ and $\exists$). The link you gave is about using the more elementary type of logic that lacks quantifiers.
In the link you gave, $A \supset B$ does not mean that $B$ is a subset of $A$. In the link, $A \supset B$ means "$A$ implies $B$". The link you gave is not about set theory.