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Summary Modelling Computing Systems Chapter 3 Faron Moller & Georg Struth
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  • Course
  • Logic for Computer Science
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  • Universiteit Utrecht (UU)
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  • Modelling Computing Systems

Logic for Computer Science/Logic for Computer Technology Chapter 3 Summary of the book Modelling Computing Systems written by Faron Moller Georg Struth. Summary written in English. Using examples and pictures, the substance and theory are clarified. Given at Utrecht University.

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  • No
  • Hoofdstuk 3
  • November 25, 2020
  • 6
  • 2020/2021
  • Summary

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  • 9781848003217
  • modelling computing systems chapter 3
  • modelling computing systems
  • faron moller georg struth
  • faron moller and georg struth
  • logic for computer science
  • computer technology logic

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Hoofdstuk 3

A monoid consist of:

- A set of A
- An element e ∈ A
- A binary operator ⊕

That satisfy the following three laws, for all x, y and z:

1. e ⊕ x = x
2. x ⊕ e = x
3. x ⊕ (y ⊕ z) = (x ⊕ y) ⊕ z

We sometimes say that e is the unit of ⊕. The third law states that the operator ⊕ is
associative(how we put the () ).



A Boolean algabra consist of:

- a set B
- Two elements, 0 ∈ B and 1 ∈ B, called the
zero and unit respectively.
- Two operators + and ·, called the sum and
product respectively.
- A unary operator ‘ called the inverse.

Figure on the right shows the different laws for
Boolean algabra.




Truth tables for Boolean algabra

, Any equation derived from the laws is known as a theorem. We can also show that for all x, we have
x + x = x.

Proof x + x = (x + x) · 1 = (x + x) · (x + x’) = x + (x · x’) = x + 0 = x

Many of these derived theorems follow use the following property. If x + y = x + z and x · y = x · z,
then y = z. In other words, if y and z ‘behave the same’ on every element x, we can conclude that y
and z are equal. We can use this to show that (x’)’ = x.

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