Intereting Posts

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Countable compact spaces as ordinals

Here’s the Karnaugh map:

The answer I should be getting from the Karnaugh should be:

- How to prove that a set of logical connectives is functionally complete(incomplete)?
- Extending the logical-or function to a low degree polynomial over a finite field
- If $B$ is an infinite complete Boolean algebra, then its saturation is a regular uncountable cardinal
- proof of functional completeness of logical operators
- Cardinality of the set of ultrafilters on an infinite Boolean algebra
- Power set representation of a boolean ring/algebra

```
T = R ∙ (CGM)'
```

I’m really not seeing how this was arrived at through any simplification methods I’ve learned thus far. I can see the answers that are intended are correct (I think), though.

From what I know, the best answer I can come up with to simplify (only) the Kargnaugh map is:

```
T=RCG'+RCM'+RC'
to:
T=R∙(CG'+CM'+C')
```

Help appreciated!

- how many semantically different boolean functions are there for n boolean variables?
- Is XOR a combination of AND and NOT operators?
- Are there further transformation principles similar to the Inclusion-Exclusion Principle (IEP)?
- proof of functional completeness of logical operators
- how to solve system of linear equations of XOR operation?
- The sum of a polynomial over a boolean affine subcube
- All finite boolean algebras have an even number of elements?
- Boolean algebras without atoms
- simplify boolean expression: xy + xy'z + x'yz'
- Extending the logical-or function to a low degree polynomial over a finite field

Using sum of products you should be able to derive:

RC’ + RCG’ + RCGM’

Substitute out the R:

R(C’ + CG’ + CGM’)

Use the identity A + A’B = A + B

R(C’ + G’ + CGM’)

That same identity works as a multivariable expression

R(C’ + G’ + M’)

Then apply DeMorgans

R(CGM)’

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- How does (ZFC-Infinity+“There is no infinite set”) compare with PA?
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- How to show the series $\displaystyle\sum_{\xi\in\mathbb Z^n}\frac{1}{(1+|\xi|^2)^{s/2}}$ converges if and only if $s>n$?