Two exercises in TRUTH TREES for negation, conjunction, and disjunction - Logic

We do two example truth trees, looking to find inconsistent sets of wffs. #Logic #PhilosophicalLogic

0:00 [Intro]
0:23 [Question #1]
3:28 [Question #2]

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In this video I introduce truth trees, inconsistent sets of wffs, and rules for disjunction, conjunction, and the negation. We talk about disjunction decomposition, conjunction decomposition, double negation, negated disjunction decomposition, and negated conjunction decomposition. Then, we do an example of a truth tree.

[QuocDatPhung]

Great video! Do you have any quick tips for solving truth trees faster? You make it look so ez but when I do it, the tree gets messy.

[paulcarello]

Exercise 1 - Given:

1. (P ∧ Q) ∨ ~R
2. ~(P ∧ Q)
3. R

From 1 and 3
(P ∧ Q) ∨ ~R
R ∴ (P ∧ Q) ... (4) ... disjunctive syllogism

From 4 and 2
(P ∧ Q) and ~(P ∧ Q) are contradictory, and cannot both be TRUE

∴ Statements are inconsistent.

[paulcarello]

Exercise 2
1. [(P ∧ Q) ∧ R]
2. ~[P ∧ (Q ∧ R)]
⇔ ~[ (P ∧ Q) ∧ R] ... associative law ... 3

from 1and 3
[(P ∧ Q) ∧ R] and ~[(P ∧ Q) ∧ R] are contradictories and cannot both be TRUE

∴ 1 and 2 are inconsistent