Question

What exactly is the relationship between truth tables and rules of inference?

score 601 · Answer 1 · 2020-03-17 00:50:55

601

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What exactly is the relationship between truth tables and rules of inference?

Published on 17 Mar 2020 - 0:50

score 82 · Answer 2 · 2020-03-19 12:51:20

82

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Exercise 2.4.5 in Chiswell and Hodges

Published on 19 Mar 2020 - 12:51

score 641 · Answer 3 · 2020-03-20 04:28:08

641

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Deriving a implies b from (not a) or b (formally: $\neg a \vee b\vdash a\rightarrow b$)

Published on 20 Mar 2020 - 4:28

score 103 · Answer 4 · 2020-03-20 19:49:17

Proving $\forall x \forall y(R(x,y) \to R(y,x)) \therefore \forall x \forall y\forall z[(R(x,y) \wedge R(x,z)) \to \exists u(R(y,u) \wedge R(z,u))]$

score 521 · Answer 5 · 2020-03-21 09:17:05

521

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Proving $A \to \exists x B(x) \therefore \exists x(A \to B(x))$

Published on 21 Mar 2020 - 9:17

score 51 · Answer 6 · 2020-03-22 22:07:28

51

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Is this proof solvable? Doubt about natural deduction

Published on 22 Mar 2020 - 22:07

score 46 · Answer 7 · 2020-03-22 22:52:13

46

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How to formalize these proofs and conclusion?

Published on 22 Mar 2020 - 22:52

score 56 · Answer 8 · 2020-03-23 16:46:15

56

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Show $\neg (W \to W), (W \leftrightarrow W) \wedge W, E \vee (W \to \neg (E \wedge W))$ are jointly inconsistent.

Published on 23 Mar 2020 - 16:46

score 285 · Answer 9 · 2020-03-23 18:08:23

285

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Prove $\forall x(A \vee B(x)) \therefore A \vee \forall xB(x)$.

Published on 23 Mar 2020 - 18:08

score 159 · Answer 10 · 2020-03-23 20:24:08

159

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Prove $\exists x (A(x) \to \forall y(A(y))$ is a theorem.

Published on 23 Mar 2020 - 20:24

score 146 · Answer 11 · 2020-03-24 13:37:21

146

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Prove $\exists x (\exists yA(y) \to A(x))$ is a theorem.

Published on 24 Mar 2020 - 13:37

score 67 · Answer 12 · 2020-03-24 22:19:50

67

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Question about Fitch style natural deduction

Published on 24 Mar 2020 - 22:19

score 179 · Answer 13 · 2020-03-30 05:29:17

179

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Language, Proof and Logic $14.12$ Solution $\left(\text{I need help}\tiny\overset{\cdot~\cdot}{\frown}\right)$

Published on 30 Mar 2020 - 5:29

score 98 · Answer 14 · 2020-04-01 00:59:33

98

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Justify indirect proof rule with law of excluded middle

Published on 01 Apr 2020 - 0:59

score 32 · Answer 15 · 2020-04-01 12:21:35

32

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Showing $(L \leftrightarrow ((N \to N) \to L)) \lor H$ is not contingent.

Published on 01 Apr 2020 - 12:21

List Question

What exactly is the relationship between truth tables and rules of inference?

Exercise 2.4.5 in Chiswell and Hodges

Deriving a implies b from (not a) or b (formally: $\neg a \vee b\vdash a\rightarrow b$)

Proving $\forall x \forall y(R(x,y) \to R(y,x)) \therefore \forall x \forall y\forall z[(R(x,y) \wedge R(x,z)) \to \exists u(R(y,u) \wedge R(z,u))]$

Proving $A \to \exists x B(x) \therefore \exists x(A \to B(x))$

Is this proof solvable? Doubt about natural deduction

How to formalize these proofs and conclusion?

Show $\neg (W \to W), (W \leftrightarrow W) \wedge W, E \vee (W \to \neg (E \wedge W))$ are jointly inconsistent.

Prove $\forall x(A \vee B(x)) \therefore A \vee \forall xB(x)$.

Prove $\exists x (A(x) \to \forall y(A(y))$ is a theorem.

Prove $\exists x (\exists yA(y) \to A(x))$ is a theorem.

Question about Fitch style natural deduction

Language, Proof and Logic $14.12$ Solution $\left(\text{I need help}\tiny\overset{\cdot~\cdot}{\frown}\right)$

Justify indirect proof rule with law of excluded middle

Showing $(L \leftrightarrow ((N \to N) \to L)) \lor H$ is not contingent.

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