Proof in Discrete math

In summary, the conversation discusses a problem involving sets and their intersections and unions. The individual has attempted to solve the problem using distribution and Venn diagrams, but their solution is incorrect. They also ask for guidance on how to approach the problem.
  • #1
brad sue
281
0
Hi, I would like some help for the following problems.

please bear with me with my special notation:
I- intersection
U- union
S- universal set
~- complement

I need to prove that: let be A and B two sets. prove
(A U B) I (A I (~B))=A

what I did is:
(A U B) I (A I (~B))

=[(A I B) U A] I [(A I B) U ~B]/distribution

=A I [(~B U A) I (~B U B)]

=A I [(~B U A) U S)

=A I (~B U A)

=(A I (~B)) U (A I A)

=AUA=A //i'm not sure here (A I (~B)) =A

problem 2

Can we conclude that A=B if A,B,C are sets such that
i) A U C = B U C
ii) A I C = B I C

how can I treat this problem?

Thank you for your help
B
 
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  • #2
I need to prove that: let be A and B two sets. prove
(A U B) I (A I (~B))=A
As stated, that's not true. (e.g. let A be any nonempty set, and let B equal A)

but that said...

(A U B) I (A I (~B))

=[(A I B) U A] I [(A I B) U ~B]/distribution
It doesn't look like you applied this rule right.

=A I [(~B U A) U S)

=A I (~B U A)
This step is wrong too.


how can I treat this problem?
I would try and draw a picture to help with my intuition.
 
  • #3
  • #4
Because it's the Calculus & Beyond forum.
 

1. What is the definition of proof in discrete math?

Proof in discrete math is a rigorous and logical demonstration that a statement or theorem is true. It involves using axioms, definitions, and previously proven theorems to show the validity of a statement.

2. What makes a proof valid in discrete math?

A proof in discrete math is considered valid if it follows a clear and organized structure, uses correct logic and reasoning, and is based on previously proven statements or definitions. It must also be able to withstand scrutiny and counterarguments.

3. How can I improve my proof-writing skills in discrete math?

To improve your proof-writing skills in discrete math, it is important to practice regularly and seek feedback from others. You can also study and analyze well-written proofs to understand the structure, flow, and reasoning behind them.

4. Can a proof in discrete math be wrong?

Yes, a proof in discrete math can be wrong if it contains incorrect or invalid statements, uses faulty logic or reasoning, or fails to consider all possible cases. It is important to thoroughly check and validate each step of a proof to ensure its correctness.

5. What are some common mistakes to avoid when writing a proof in discrete math?

Some common mistakes to avoid when writing a proof in discrete math include using vague language, making unwarranted assumptions, skipping steps, and using circular reasoning. It is also important to avoid making careless errors and to carefully check each step of the proof for accuracy.

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