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Uitgewerkte oefeningen (voorbeeldexamenvragen) Predikatenlogica - PL1 -17/20 in 1e zit!

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Dit document omvat 28 uitgewerkte bewijzen/redeneringen in PL1 (predikatenlogica). De oefeningen komen uit de voorbeeldexamens Logica en Wetenschapsfilosofie van voorbije jaren gedoceerd door prof. Van Bendegem en prof. Van Kerkhove en zijn nagekeken en verbeterd door de assistent. In mijn examenjaar en ook in het jaar (bevestigd door een vriendin die haar examen in dit jaar nam) kwam de vraag van PL1 (1 van de 4 examenvragen) EXACT uit dit document - een ideale voorbereiding voor je examen dus! Ik behaalde voor dit opleidingsonderdeel 17/20.

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Marie C.


Oefeningen PL1 – predikatenlogica
Het bestand bevat volgende uitgewerkte oefeningen
1) (∃x)(Px ⊃ Qx), (∀x)∼Qx ⊢∼(∀x)Px
2) (∀x)Px ⊢ (∃x)(Rx ⊃ (Px v Qx))
3) (∃x)Px ⊢ (∃x)(Rx ⊃ (Px v Qx))
4) ∼(∃x)Px, (∀x)(∼Px ⊃ Qx) ⊢ (∃x)Qx
5) (∃x)(Px & Qx), (∀x)((Px v Qx) ⊃ Rx) ⊢ (∃x)Rx
6) (∀x)(Px & Qx), (∀x)(Rx ⊃∼Qx) ⊢∼(∃x)Rx
7) (∀x)(Px & Qx), (∃x)(Px ⊃ Rx) ⊢ (∃x)Rx
8) ∼(∀x)Px, (∀x)Qx ⊢ (∃x)(∼Px & Qx)
9) ∼(∃x)Px ⊢ (∀x)(Px ⊃∼Px)
10) (∃x)(Px⊃Qx), (∀x)(Px ⊃∼Qx)⊢∼(∀x)Px
11) (∃x)∼Px, (∀x)(∼Qx⊃Px) ⊢(∃x)Qx
12) (∀x)Px& (∃x)Qx, (∀x)(Qx ⊃Rx)⊢(∃x)(Px& Rx)
13) (∃x)(Px)v (∃x)(Qx)⊢(∃x)(Px v Qx)
14) (∃x)(Px& Qx)⊢(∃x)(Px) &(∃x)(Qx)
15) (∃x)∼(∼Px v Qx) ⊢(∃x)(Px& ∼Qx)
16) (∃x)∼Px ⊢(∃x)(Px ⊃Qx)
17) ~(∀x)(Px⊃Qx) ⊢(∃x)(Px & ~Qx)
18) (∀x)(Px⊃Qx), (∀x)(Px v Qx) ⊢ (∃x)Qx
19) (∀x)(Px⊃(Qx & Rx)), (∃x)(Px v Qx) ⊢ (∃x)Qx
20) (∀x)(Px⊃~Qx) ) ⊢ ~(∃x)(Px & Qx)
(∀x)(Px⊃~Qx) ) ⊢ (∀x)~(Px & Qx)
21) (∃x)(Px⊃~Qx) ⊢ ~(∀x)Px
22) (∀x)(Px⊃(Qx & Rx)), (∃x)~Qx ⊢ (∃x)~Px
23) ⊢ (∀x)(Px ⊃ Qa) = (∃x)(Px) ⊃ Qa
24) ⊢ (∀x)(Pa ⊃ Qa) = (Pa ⊃ (∀x)Qx )
25) (x)(Px  Qx), (x)Qx ⊢ (x)Px
26) (∃x)(Px) ⊢ (x)~Px
27) (x)~Px ⊢ ~(∃x)Px
28) (x)Px ⊢ ~(∃x)~Px

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