2018-12-22

Propositional logic: exercises

Exercises

Some exercises to train propositional logic.

If anyone sees an error please raise an issue in the blog repository, thanks :).

Exercise 1

Let’s consider a propositional language where:

  • p: Is Monday

  • q: John goes running

  • r: Elsa goes running

Formalize the following sentences:

If it’s Monday, John and Elsa go running
— A
If it’s Monday John goes running
— B
If it’s other day than Monday, Elsa goes running, but John doesn’t
— C

Solutions:

15cf1d5e3870ce537725c72f59ba8b51.png
Figure 1. Solution to A
4746161d80e6233cd4e033b11d76f630.png
Figure 2. Solution to B
2869e7f1a17332d42352718625fea878.png
Figure 3. Solution to C

Table of truth

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Figure 4. table of truth

Exercise 2

Let’s consider a propositional language where:

  • p: John buys lottery tickets

  • q: Is Christmas time

  • r: John feels lucky

Formalize the following sentences:

If is Christmas time, or John feels lucky, then John buys lottery tickets
— A
If it’s not Christmas, and John doesn’t feel lucky, he doesn’t buy lottery
— B

Solutions:

644cc113c4e2e43fed228da526309215.png
Figure 5. Solution to A
4a9b2fa4c9f484a58c366527cf3744de.png
Figure 6. Solution to B

Table of truth

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Figure 7. table of truth