Post on 17-Jan-2016
Introductory LogicPHI 120
Presentation: "Truth Tables – Validity vs. Soundness"
This PowerPoint Presentation contains a large number of slides, a good many of which are nearly identical. If you print
this Presentation, I recommend six or nine slides per page.
Homework1. Study Allen/Hand Logic Primer– Sec. 1.1, p. 2: “soundness”– Sec. 2.2, p. 45, “incompatible premises”
2. Ex. 2.2: i-xii
VALIDITY vs. SOUNDNESSP & Q, ~P ⊢ R
Validity: An argument is valid if and only if:• if all of its premises are true• its conclusion is true.
Corollary: It is impossible for a valid argument to have:• all true premises• false conclusion
Validity vs. Soundness
Valid Argument• No invalidating
assignment
Criteria of a Sound Argument1. argument is valid
and
2. all premises are True.
Valid but Unsound no invalidating
assignment not all premises true
Invalidating Assignment (1) conclusion is False (2) all premises are True
Incompatible PremisesP Q R P & R , ~ P ⊢ Q
Incompatible PremisesP Q R P & R , ~ P ⊢ Q
Atomic statements MUST be written in alphabetical order
Incompatible PremisesP Q R P & R , ~ P ⊢ Q
Incompatible PremisesP Q R P & R , ~ P ⊢ QTTTTFFFF
Incompatible PremisesP Q R P & R , ~ P ⊢ QT TT TT FT FF TF TF FF F
Incompatible PremisesP Q R P & R , ~ P ⊢ QT T TT T FT F TT F FF T TF T FF F TF F F
Incompatible PremisesP Q R P & R , ~ P ⊢ QT T TT T FT F TT F FF T TF T FF F TF F F
Incompatible PremisesP Q R P & R , ~ P ⊢ QT T TT T FT F TT F FF T TF T FF F TF F F
Incompatible PremisesP Q R P & R , ~ P ⊢ QT T T FT T F FT F T FT F F FF T T TF T F TF F T TF F F T
Incompatible PremisesP Q R P & R , ~ P ⊢ QT T T FT T F FT F T FT F F FF T T TF T F TF F T TF F F T
Incompatible PremisesP Q R P & R , ~ P ⊢ QT T T FT T F F FT F T FT F F FF T T TF T F TF F T TF F F T
Incompatible PremisesP Q R P & R , ~ P ⊢ QT T T FT T F F FT F T FT F F F FF T T TF T F TF F T TF F F T
Incompatible PremisesP Q R P & R , ~ P ⊢ QT T T FT T F F FT F T FT F F F FF T T F TF T F TF F T TF F F T
Incompatible PremisesP Q R P & R , ~ P ⊢ QT T T FT T F F FT F T FT F F F FF T T F TF T F F TF F T TF F F T
Incompatible PremisesP Q R P & R , ~ P ⊢ QT T T FT T F F FT F T FT F F F FF T T F TF T F F TF F T F TF F F T
Incompatible PremisesP Q R P & R , ~ P ⊢ QT T T FT T F F FT F T FT F F F FF T T F TF T F F TF F T F TF F F F T
Incompatible PremisesP Q R P & R , ~ P ⊢ QT T T T FT T F F FT F T T FT F F F FF T T F TF T F F TF F T F TF F F F T
Incompatible PremisesP Q R P & R , ~ P ⊢ QT T T T FT T F F FT F T T FT F F F FF T T F TF T F F TF F T F TF F F F T
Testing for Validity:
Find the Invalidating Assignment
Incompatible PremisesP Q R P & R , ~ P ⊢ QT T T T FT T F F FT F T T FT F F F FF T T F TF T F F TF F T F TF F F F T
Incompatible PremisesP Q R P & R , ~ P ⊢ QT T T T FT T F F FT F T T F FT F F F FF T T F TF T F F TF F T F TF F F F T
Incompatible PremisesP Q R P & R , ~ P ⊢ QT T T T FT T F F FT F T T FT F F F F FF T T F TF T F F TF F T F TF F F F T
Incompatible PremisesP Q R P & R , ~ P ⊢ QT T T T FT T F F FT F T T FT F F F FF T T F TF T F F TF F T F T FF F F F T
Incompatible PremisesP Q R P & R , ~ P ⊢ QT T T T FT T F F FT F T T FT F F F FF T T F TF T F F TF F T F TF F F F T F
P Q R P & R , ~ P ⊢ QT T T T FT T F F FT F T T FT F F F FF T T F TF T F F TF F T F TF F F F T
No Invalidating Assignment
So the argument is valid
Incompatible Premises
Incompatible PremisesP Q R P & R , ~ P ⊢ QT T T T FT T F F FT F T T FT F F F FF T T F TF T F F TF F T F TF F F F T
p. 45
Validity vs. Soundness
Valid Argument• Impossible for
conclusion to be False and all premises True
Sound Argument• An argument is sound if
and only if it is valid and all its premises are true.
Valid but Unsound
No invalidating assignment
Not all premises true
SEQUENTSTruth Tables
Determine truth-values of:
1. atomic statements2. negations of atomics
3. inside parentheses4. negation of the parentheses
5. any remaining connectives
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ~Q⊢
First, identify the governing connectives.
~P, R v ~P <-> P v Q ~Q⊢
First, identify the governing connectives.
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ~Q⊢
First, identify the governing connectives.
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, (R v ~P) <-> (P v Q) ~Q⊢
The second premise is a complex binary: Φ <-> Ψ
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QThe conclusion is a negation.
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
CONSTRUCT THE TRUTH TABLETruth Tables – Sequents
~P, R v ~P <-> P v Q ~Q⊢Determine the number of rows for the sequent
23 simple statements = 8 rows
~P, R v ~P <-> P v Q ⊢ ~Q~ P , R v ~ P <-> P v Q ⊢ ~ Q _ __
Valid
____Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ Q _ __
Valid
____Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ Q _ __
Valid
____Invalid
Alphabetical Sequence!
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ Q _ __
Valid
____Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QTTTTFFFF
_ __Valid
____Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QT TT TT FT FF TF TF FF F
_ __Valid
____Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QT T TT T FT F TT F FF T TF T FF F TF F F
_ __Valid
____Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QT T T F FT T F F FT F T F FT F F F FF T T T TF T F T TF F T T TF F F T T
_ __Valid
____Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QT T T F F FT T F F F FT F T F F TT F F F F TF T T T T FF T F T T FF F T T T TF F F T T T
_ __Valid
____Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QT T T F F FT T F F F FT F T F F TT F F F F TF T T T T FF T F T T FF F T T T TF F F T T T
_ __Valid
____Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
(R v ~P) <-> (P v Q)
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QT T T F F FT T F F F F FT F T F F TT F F F F F TF T T T T FF T F T T FF F T T T TF F F T T T
_ __Valid
____Invalid
(R v ~P) <-> (P v Q)
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QT T T F F FT T F F F F FT F T F F TT F F F F F TF T T T T FF T F T T FF F T T T TF F F T T T
_ __Valid
____Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QT T T F T F FT T F F F F FT F T F T F TT F F F F F TF T T T T T FF T F T T T FF F T T T T TF F F T T T T
_ __Valid
____Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QT T T F T F FT T F F F F FT F T F T F TT F F F F F TF T T T T T FF T F T T T FF F T T T T F TF F F T T T F T
_ __Valid
____Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QT T T F T F FT T F F F F FT F T F T F TT F F F F F TF T T T T T FF T F T T T FF F T T T T F TF F F T T T F T
_ __Valid
____Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QT T T F T F T FT T F F F F T FT F T F T F T TT F F F F F T TF T T T T T T FF T F T T T T FF F T T T T F TF F F T T T F T
_ __Valid
____Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QT T T F T F T FT T F F F F F T FT F T F T F T TT F F F F F F T TF T T T T T T FF T F T T T T FF F T T T T F F TF F F T T T F F T
_ __Valid
____Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QT T T F T F T FT T F F F F F T FT F T F T F T TT F F F F F F T TF T T T T T T FF T F T T T T FF F T T T T F F TF F F T T T F F T
_ __Valid
____Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QT T T F T F T T FT T F F F F F T FT F T F T F T T TT F F F F F F T TF T T T T T T T FF T F T T T T T FF F T T T T F F TF F F T T T F F T
_ __Valid
____Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QT T T F T F T T FT T F F F F F T FT F T F T F T T TT F F F F F F T TF T T T T T T T FF T F T T T T T FF F T T T T F F TF F F T T T F F T
_ __Valid
____InvalidTesting for Validity:
Find the Invalidating Assignment
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QT T T F T F T T FT T F F F F F T FT F T F T F T T TT F F F F F F T TF T T T T T T T FF T F T T T T T FF F T T T T F F TF F F T T T F F T
_ __Valid
____Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QT T T F T F T T FT T F F F F F T FT F T F T F T T TT F F F F F F T TF T T T T T T T FF T F T T T T T FF F T T T T F F TF F F T T T F F T
_ __Valid
____Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QT T T F T F T T FT T F F F F F T FT F T F T F T T TT F F F F F F T TF T T T T T T T FF T F T T T T T FF F T T T T F F TF F F T T T F F T
_ __Valid
____Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QT T T F T F T T FT T F F F F F T FT F T F T F T T TT F F F F F F T TF T T T T T T T FF T F T T T T T FF F T T T T F F TF F F T T T F F T
_ __Valid
____Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QT T T F T F T T FT T F F F F F T FT F T F T F T T TT F F F F F F T TF T T T T T T T FF T F T T T T T FF F T T T T F F TF F F T T T F F T
_ __Valid
__Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QT T T F T F T T FT T F F F F F T FT F T F T F T T TT F F F F F F T TF T T T T T T T FF T F T T T T T FF F T T T T F F TF F F T T T F F T
Tautology Inconsistency Contingency
_ __Valid
__Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
~P, R v ~P <-> P v Q ⊢ ~QP Q R ~ P , R v ~ P <-> P v Q ⊢ ~ QT T T F T F T T FT T F F F F F T FT F T F T F T T TT F F F F F F T TF T T T T T T T FF T F T T T T T FF F T T T T F F TF F F T T T F F T
Tautology Inconsistency Contingency
_ __Valid
__Invalid
Truth TablesDirections: (i) Construct a Truth Table in the grids provided. (ii) Circle the governing connective in each sentence. (iii) If the sequent is invalid, circle the invalidating assignment and check the line which reads INVALID. If the sequent is valid, check the line which reads VALID. (iv) In the space provided, identify what kind of truth value the conclusion has: Tautology, Inconsistency, or Contingency.
Homework1. Study Allen/Hand Logic Primer– Sec. 1.1, p. 2: “soundness”– Sec. 2.2, p. 45, “incompatible premises”
2. Ex. 2.2: i-xii