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Logic eighteen valid argument forms problems
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- 2020 год
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Task 1
Just write the sentence forms for which the two sentences below are a substitution instance. You don't have to write out the sentence form--just the letter which precedes it.
1. ~ ~ [ ( A v ~A) v ~ ~ B]
2. ~ ~A --> ~ (~ B --> C)
Task 2
For each of the following expressions indicate (1) which variables are free and which bound; (2) which letters serve as individual constants and which as property constants; (3) which free variables are within the scope of some quantifier or other and which individual constants are not within the scope of any quantifier.
1. (x) (Fx -> Ga)
2. (x) [Fx -> (Gy -> Hx)]
3. Fa v (x) [ (Ga v Dx) -> (~Ky•Hb) ]
Task 3
Using the eighteen valid argument forms, prove that the following arguments are valid. f(These proofs are very basic. None requires more than six additional lines to complete).
(13) 1. (AB)v(CD)
2. ~A/C
(15) 1. (AB)->C
2. A~C/~B
Task 4
Prove valid using the eighteen valid argument forms. (These proofs are moderately difficult. They will require between six and fifteen additional lines to complete.)
(1) 1. (AB)->R
2. A
3. C->~R/~(CB)
(3) 1. (AH)->(MN)
/(AH)->N
(5) 1. H->K
2. (KL)->M/L->(H->M)
(11) 1. AvB
2. C
3. (AC)->D
4. ~(~FB)/DvF
(13) 1. ~(DvC)
2. ~C->(A->~B)
3. A=B/~A
Отвеченные вопросы приведены в содержании.
Нету.
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