- 351 Views
- Uploaded on
- Presentation posted in: Sports / GamesEducation / CareerFashion / BeautyGraphics / DesignNews / Politics

TF truth, falsity, and indeterminacy

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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

TF truth, falsity, and indeterminacy

P is truth-functionally true iff it has the value T for any truth-value assignment.

P is truth-functionally false iff it has the value F for any truth-value assignment.

P is tf-false iff ~P is tf-true

P is truth-functionally indeterminate iff it has the value T for some truth-value assignments, and the value F for some other truth-value assignments.

P is tf-indeterminate iff it is neither tf-true nor th-false.

TF equivalence and consistency

P and Q are truth-functionally equivalent iff P and Q do not have different truth-values for any truth-value assignment.

A set of sentences is truth-functionally consistent iff there is a truth-value assignment that on which all the members of the set have the value T.

A set of sentences is truth-functionally inconsistent iff it is not tf-consistent.

TF entailment and validity

A set of SL sentences truth-functionally entails a sentence P iff there is no truth-value assignment on which every member of is true and P false.

TF entailment and validity

A set of SL sentences truth-functionally entails a sentence P iff there is no truth-value assignment on which every member of is true and P false.

An argument of SL is truth-functionally valid iff there is no truth-value assignment on which all the premises are true and the conclusion false.

TF entailment and validity

A set of SL sentences truth-functionally entails a sentence P iff there is no truth-value assignment on which every member of is true and P false.

An argument of SL is truth-functionally valid iff there is no truth-value assignment on which all the premises are true and the conclusion false.

An argument of SL is truth-functionally invalid iff it is not tf-valid.

TF entailment and validity

An argument of SL is truth-functionally valid iff there is no truth-value assignment on which all the premises are true and the conclusion false.

An argument of SL is truth-functionally invalid iff it is not tf-valid.

An argument is tf-valid iff the premises tf-entail the conclusion.

TF properties

P is truth-functionally true iff it has the value T for any truth-value assignment.

P is truth-functionally false iff ~P is tf-true.

P is truth-functionally indeterminate iff P is neither tf-true nor tf-false.

P and Q are truth-functionally equivalent iff P and Q do not have different truth-values for any truth-value assignment.

A set of sentences is truth-functionally consistent iff there is a truth-value assignment that on which all the members of the set have the value T.

3.2E 1j

3.2E 1j

3.2E 1j

3.2E 1j

3.2E 1j

3.2E 1l

3.2E 1l

3.2E 1l

3.2E 1l

3.2E 1l

3.3E 1d

3.3E 1d

3.3E 1d

3.3E 1d

3.3E 1d

3.3E 1d

3.3E 1d

3.3E 1d

3.3E 1d

3.4E 1f

3.4E 1f

3.5E1b

3.5E1b

3.5E1b

3.5E1b

3.5E1b

3.5E1b

3.5E1b

3.5E1b

3.5E1b

3.5E1b

3.5E1b

3.5E1b

3.5E1b

3.5E1b

Show that ~B(B&~B) is not tf-true

shortened truth tables

Show that ~B(B&~B) is not tf-true

shortened truth tables

Show that ~B(B&~B) is not tf-true

shortened truth tables

Show that ~B(B&~B) is not tf-true

shortened truth tables

Show that ~B(B&~B) is not tf-true

shortened truth tables

Show that ~B(B&~B) is not tf-true

shortened truth tables

Show that (~B~A)&C is not tf-false

shortened truth tables

Show that (~B~A)&C is not tf-false

shortened truth tables

Show that (~B~A)&C is not tf-false

shortened truth tables

Show that (~B~A)&C is not tf-false

shortened truth tables

Show that (~B~A)&C is not tf-false

shortened truth tables

Show that (~B~A)&C is not tf-false

shortened truth tables

Show that (~B~A)&C is not tf-false

shortened truth tables

Show that (~B~A)&C is not tf-false

shortened truth tables

Show that (AB) (BA) is not tf-false

shortened truth tables

Show that (AB) (BA) is not tf-false

shortened truth tables

Show that (AB) (BA) is not tf-false

shortened truth tables

Show that (AB) (BA) is not tf-false

COTRADICTION!

shortened truth tables

Show that (AB) (BA) is not tf-false

shortened truth tables

Show that (AB) (BA) is not tf-false

shortened truth tables

Show that (AB) (BA) is not tf-false

shortened truth tables

Show that (AB) (BA) is not tf-false

CONTRADICTION!

shortened truth tables

Show that (AB) (BA) is not tf-false

shortened truth tables

Show that (AB) (BA) is not tf-false

shortened truth tables

Show that (AB) (BA) is not tf-false

shortened truth tables

Show that (AB) (BA) is not tf-true

shortened truth tables

Show that (AB) (BA) is not tf-true

shortened truth tables

Show that (AB) (BA) is not tf-true

shortened truth tables

Show that (AB) (BA) is not tf-true

CONTRADICTION!

Therefore, the sentence is tf-true

shortened truth tables

Practice

Show that:

{A(B&C), B (AC), C~C} is tf-consistent

{B(A&~C), (CA) B, ~BA} ~(AC)

shortened truth tables

Practice

Show that:

{A(B&C), B (AC), C~C} is tf-consistent

{B(A&~C), (CA) B, ~BA} ~(AC)

shortened truth tables

Practice

Show that:

{A(B&C), B (AC), C~C} is tf-consistent

{B(A&~C), (CA) B, ~BA} ~(AC)

shortened truth tables

Practice

Show that:

{A(B&C), B (AC), C~C} is tf-consistent

{B(A&~C), (CA) B, ~BA} ~(AC)

shortened truth tables

Practice

Show that:

{A(B&C), B (AC), C~C} is tf-consistent

{B(A&~C), (CA) B, ~BA} ~(AC)

shortened truth tables

Practice

Show that:

{A(B&C), B (AC), C~C} is tf-consistent

{B(A&~C), (CA) B, ~BA} ~(AC)

shortened truth tables

Practice

Show that:

{A(B&C), B (AC), C~C} is tf-consistent

{B(A&~C), (CA) B, ~BA} ~(AC)

shortened truth tables

Practice

Show that:

{A(B&C), B (AC), C~C} is tf-consistent

{B(A&~C), (CA) B, ~BA} ~(AC)

shortened truth tables

Practice

Show that:

{A(B&C), B (AC), C~C} is tf-consistent

{B(A&~C), (CA) B, ~BA} ~(AC)

shortened truth tables

Practice

Show that:

{A(B&C), B (AC), C~C} is tf-consistent

{B(A&~C), (CA) B, ~BA} ~(AC)

shortened truth tables

Practice

Show that:

{A(B&C), B (AC), C~C} is tf-consistent

{B(A&~C), (CA) B, ~BA} ~(AC)

shortened truth tables

Practice

Show that:

{A(B&C), B (AC), C~C} is tf-consistent

{B(A&~C), (CA) B, ~BA} ~(AC)

shortened truth tables

Practice

Show that:

{A(B&C), B (AC), C~C} is tf-consistent

{B(A&~C), (CA) B, ~BA} ~(AC)