nida
Uploaded by
6 SLIDES
199 VUES
60LIKES

Logical Reasoning and Propositions in Plain English

DESCRIPTION

Understand logic in propositions, connectives, and translations. Learn formalizing arguments with propositional variables. Explore tautologies, contradictions, and logical equivalence.

1 / 6

Télécharger la présentation

Logical Reasoning and Propositions in Plain English

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CA 208 Logic Ex1 • In your own words, define the following • Logic: • Valid reasoning/inference (2 equivalent definitions): • Propositions/statements: • List the • 4 binary • 1 unary connectives (use the special symbols) • Translate the following into plain English • P |= C • {A,B} |= A  B • {A  B} |= A • {A, A → B} |= B

  2. CA 208 Logic Ex1 • Formalise the following arguments/inferences using proposional variables (P, Q, R, ...) and the logical connectives. State the translation keys: • Kate is a student. If Kate is a student, then Kate is broke. |= Kate is broke. • Kate is a student. Kate is broke. |= Kate is a student and Kate is broke. • Kate is a student and Kate is broke. |= Kate is a student. • Kate is a student. |= Kate is a student. • Kate is taller than John. John is taller than Mike. If Kate is taller than John and John is taller than Mike, then Kate is taller than Mike. |= Kate is taller than Mike. • Intutively, are the inferences above logically valid (i.e. is the conclusion true in all situations where the premises are true)? • Is the following inference logically valid? • If Kate is a student, then Kate is broke. Kate is broke. (|= ??) Kate is a student.

  3. CA 208 Logic Ex1 Complete the following truth tables:

  4. CA 208 Logic Ex2 • What are • Tautologies • Contradictions • Contingencies • Define logical equivalence  in terms of  • Intuitively, what does it mean for two formulas to be logically equivalent?

  5. CA 208 Logic Ex2 • Use the truth table method to show whether the following are tautologies, contingencies or contradictions • (P  (P Q))  Q • (P  Q)  (PQ) • (Q  Q) • Use the truth table method and the definition of logical equivalence in terms of the biconditional (iff) to show that • (P  Q)  (P  Q)

  6. CA 208 Logic Ex2 • Use the Boolean equivalences to show (i.e.rewrite) that the following are logically equivalent: • (Q  P)  (PQ) • (P  (Q  P))  (P  Q)

More Related