Interactive problem sets for deductive logic courses.
Developed for Harvard's introductory course.
Example problems below
Truth table, truth-functional paraphrase, implication, disjunctive normal form, natural language argument, quantificational paraphrase, quantificational interpretation.
In progress
Deduction problems.
1.
Construct a truth table for p ∨ r ≡ q ∨ r
p | q | r | p ∨ r ≡ q ∨ r |
⊤ | ⊤ | ⊤ | |
⊤ | ⊤ | ⊥ | |
⊤ | ⊥ | ⊤ | |
⊤ | ⊥ | ⊥ | |
⊥ | ⊤ | ⊤ | |
⊥ | ⊤ | ⊥ | |
⊥ | ⊥ | ⊤ | |
⊥ | ⊥ | ⊥ |
2.
Construct a truth table for –p ∨ q ≡ (p ⊃ r)
p | q | r | –p ∨ q ≡ (p ⊃ r) |
⊤ | ⊤ | ⊤ | |
⊤ | ⊤ | ⊥ | |
⊤ | ⊥ | ⊤ | |
⊤ | ⊥ | ⊥ | |
⊥ | ⊤ | ⊤ | |
⊥ | ⊤ | ⊥ | |
⊥ | ⊥ | ⊤ | |
⊥ | ⊥ | ⊥ |
3.
Paraphrase the following sentence in logical notation:
If Serbia is forced to submit, then Austria-Hungary will control the Balkans and threaten Constantinople if and only if England does not intervene.
4.
Does schema (1) imply schema (2)?
If implication fails to hold, provide an interpretation that witnesses this fact.
p | q | r | [p ≡ q ≡ r] ⊃ [p ∙ –q ∨ –p ∙ r] |
⊤ | ⊤ | ⊤ | |
⊤ | ⊤ | ⊥ | |
⊤ | ⊥ | ⊤ | |
⊤ | ⊥ | ⊥ | |
⊥ | ⊤ | ⊤ | |
⊥ | ⊤ | ⊥ | |
⊥ | ⊥ | ⊤ | |
⊥ | ⊥ | ⊥ |
p | q | r |
5.
Determine whether schema (1) and schema (2) are equivalent:
If equivalence fails to hold, provide an interpretation that witnesses this fact.
p | q | r | [p ≡ q ≡ r] ≡ [p ∙ q ∙ r ∨ –p ∙ –q ∙ –r] |
⊤ | ⊤ | ⊤ | |
⊤ | ⊤ | ⊥ | |
⊤ | ⊥ | ⊤ | |
⊤ | ⊥ | ⊥ | |
⊥ | ⊤ | ⊤ | |
⊥ | ⊤ | ⊥ | |
⊥ | ⊥ | ⊤ | |
⊥ | ⊥ | ⊥ |
p | q | r |
6.
Transform the following schema into disjunctive normal form:
7.
For the following argument, paraphrase the premises and conclusion and also determine whether the premises truth-functionally imply the conclusion.
8.
Paraphrase the following sentence in logical notation:
Use the following predicates:
9.
Specify an interpretation that makes the following schema true:
10.
Specify an interpretation that makes the following schema true, and an intrepretation that makes it false: