derivations

5/18/09 10Software

Skills to be acquired in this tutorial:

Proving an argument to be valid by displaying a derivation. Simple sentential derivations using some of the Rules of Inference.

Reading

Bergmann[2004] The Logic Book Section 5.1.

The Tutorial:

If you suspect that an symbolized argument might be valid, you should attempt to give a derivation of it.

A derivation is a proof of validity.

Roll your own derivations

6/21/07 10 Software

You may have derivations of your own that you wish to try. Just type, paste, or drag and drop, them into the panel, select your derivation, and click 'Start from selection'.

[Often copy-and-paste won't work directly from a Web Page; however, usually drag-and-drop will work!]

You will need to use the correct logical symbols. Here they are

F ∴ F . G ∼ ∧ ∨ ⊃ ≡ ∃ ∴

Rules for the Copi System

1/8/26 under construction

12/28/20

Roll your own derivations

You may have derivations of your own that you wish to try. Just type, paste, or drag and drop, them into the panel, select your derivation, and click 'Start from selection'.

[Often copy-and-paste won't work directly from a Web Page; however, usually drag-and-drop will work!]

You will need to use the correct logical symbols. Here they are

F ∴ F ∧ G ∼ ∧ ∨ ⊃ ≡ ∀ ∃ ∴

Tutorial 6: Abelian Groups Tutorial 7: Boolean Algebra Tutorial 8: Linearly Ordered Sets Coming sometime!

1/2/2021

Solutions

Theorem 1

Theorem 2

1/17/20

1/17/20

12/23/20

Tutorial 5: Number Theory II

Formal Number Theory. Just more theorems for you.

Recall

Formal Number Theory has five proper symbols {=,',+, .,0} and six proper axioms

(∀x)(∀y)(x'=y'⊃x=y),
(∀x)~(x'=0),
(∀x)(x+0=x),
(∀x)(∀y)(x+y'=(x+y)'),
(∀x)(x.0=0),
(∀x)(∀y)(x.y'=x.y+x)

And the axiom (metalanguage) schema of induction. If φ[n] is any formula in the object language with free variable n then

(φ[0]∧(∀n)(φ[n]⊃φ[n'])) ⊃ (∀n)φ[n]