Discrete Structures, Logic, and Computability by Hein James L. & Hein James L

Author:Hein, James L. & Hein, James L.
Language: eng
Format: epub
Publisher: Jones & Bartlett Learning
Published: 2015-12-13T05:00:00+00:00

Example 6 Part of an Equivalence

We’ll give an indirect formal proof of the following statement:

∀x ¬ W(x) → ¬ ∃x W(x).

We’ll prove the converse of ∀x ¬ W(x) → ¬ ∃x W(x) in Example 15.

Example 7 Using Hypothetical Syllogism

We’ll prove the following statement:

∀x (A(x) → B(x)) ∧ ∀x (B(x) → C (x)) → ∀x (A(x) → C (x)).

Example 8 Lewis Carroll’s Logic

The following argument is from Symbolic Logic by Lewis Carroll.

Babies are illogical. Nobody is despised who can manage a crocodile.

Illogical persons are despised. Therefore babies cannot manage crocodiles.

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