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10/29/06 Applet removed 2013

Quiz 8 Applet

This contains an applet, so it will be slow loading and likely it will ask you about security.

2013

The Tutorial

Existential Instantiation permits you to remove an existential quantifier from a formula which has an existential quantifier as its main connective. It is one of those rules which involves the adoption and dropping of an extra assumption (like ∼I,⊃I,∨E, and ≡I).

The circumstance that Existential Instantiation gets invoked looks like this.

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The Tutorial

There is a rule for adding a Existential Quantifier. This permits the step illustrated by the following proof fragments.

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The Tutorial

There also is a rule for adding a Universal Quantifier. This permits the step illustrated by the following proof fragments.

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Skill to be acquired:

To understand the concepts of scope, free, bound. To meet substitution and a simplified version of the rule for removing a Universal Quantifier.

Quiz 7 Invalidity

10/30/06 Quiz 7 was formerly known as Quiz 4

Quiz 7 Invalidity

[This has been done in the downloadable application, but the principles apply to the applet version also.]

Quiz 7.

10/29/06 [applet removed 2013]

This contains an applet, so it will be slow loading and likely it will ask you about security.

Quiz 7 Applet

The later parts of this can be quite difficult, so it is configured in such a way that the bulk of the work and marks are on intermediate level material. [There is a small quantity of the more challenging material to engage the advanced students.]

Under revision 2013

The Tutorial

We will certainly wish to discuss the truth and falsity of formulas with quantifiers in them.

Let us start with an Interpretation

Interpretation 1

Universe= {a,b}
F={a}

Tutorial 16 Symbolization using the quantifiers.

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Skill to be acquired in this tutorial:

To learn how to use the Universal and Existential Quantifiers in symbolizing propositions.

The Tutorial

In Predicate Logic there are two new logical connectives, the Universal Quantifier (∀x) and the Existential Quantifier (∃x). These are used for symbolizing certain English constructions (they also have their own rules of inference and their own semantics, which we will learn about later).