Why Is DeMorgan's Theorem Valid According to Truth Tables?

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Discussion Overview

The discussion centers around demonstrating the validity of DeMorgan's theorem using truth tables, specifically for two variables. Participants seek clarification on constructing the truth table and applying the theorem correctly.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant requests assistance in understanding how to populate a truth table for DeMorgan's theorem, expressing confusion about where to place 0's and 1's.
  • Another participant suggests that the truth table should have four columns: X, Y, X'Y', and X' + Y', indicating a potential misunderstanding in the initial setup.
  • There is a mention of a possible typo in the statement of DeMorgan's Law, though specifics are not provided.
  • A hint is provided to check external resources, such as Wikipedia, for further clarification on DeMorgan's Law.

Areas of Agreement / Disagreement

Participants appear to agree on the need for a truth table to demonstrate DeMorgan's theorem, but there is uncertainty regarding the correct setup and application of the theorem. The discussion remains unresolved as participants seek clarification.

Contextual Notes

There is a lack of clarity on how to correctly apply DeMorgan's theorem in the context of the truth table, and participants have not fully resolved the details of the theorem's statement.

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1. Demonstrate by means of truth tables the validity of the following identities.

a) DeMorgan's theorem for two variables

X'Y' = X' + Y'

' is the bars that are above the letters.




Can someone explain this to me? I mean the truth table is just going to look like this: X'Y' X' Y'
I just need to know where and 0's and 1's go and why. Seems so easy, but I haven't been able to understand it.
 
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XodoX said:
1. Demonstrate by means of truth tables the validity of the following identities.

a) DeMorgan's theorem for two variables

X'Y' = X' + Y'

' is the bars that are above the letters.




Can someone explain this to me? I mean the truth table is just going to look like this: X'Y' X' Y'
I just need to know where and 0's and 1's go and why. Seems so easy, but I haven't been able to understand it.

Your table will have 4 coulmns. Fist is X, second is Y, third is X'Y' and forth is X' + Y'.

Well, except that I think you forgot something in your statement of DeMorgan's Law.

EDIT -- it's just a typo in how you wrote it out...
 
berkeman said:
Your table will have 4 coulmns. Fist is X, second is Y, third is X'Y' and forth is X' + Y'.

Well, except that I think you forgot something in your statement of DeMorgan's Law.

EDIT -- it's just a typo in how you wrote it out...


Thanks. I just thought it was 3. How do I find out about the 0's and 1's ? I know DeMorgan's but don't know how to apply it to this one.
 
XodoX said:
Thanks. I just thought it was 3. How do I find out about the 0's and 1's ? I know DeMorgan's but don't know how to apply it to this one.

(hint -- check out the wikipedia.org page on DeMorgan's Law...)
 

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