The Language of Argument

1 4 1

C o n d i t i o n a l s

Two more classic, common, and useful argument forms combine conditionals

with disjunction. Using truth tables, test them for validity.

Constructive Dilemma Destructive Dilemma

p ∨ q ~p ∨ ~q

p ⊃ r r ⊃ p

q ⊃ r r ⊃ q

∴ r ∴ ~r

Exercise XXIII

Using the truth table techniques employed above, test the following argument

forms for validity. (For your own entertainment, guess whether the argument

form is valid or invalid before working it out.)

1.  p ⊃ q
   ∴ q ⊃ p
   2.  p ⊃ q
   ∴ ~q ⊃ ~p


2. ~q ⊃ ~p
   ∴ p ⊃ q
   4.  p ⊃ q
   q ⊃ r
   ∴ p ⊃ (q & r)


3.  p ⊃ q
   q ⊃ r
   ~r
   ∴ ~p


4.  p ⊃ q
   q ⊃ r
   ∴ ~r ⊃ ~p


5. p ∨ q
   p ⊃ q
   q ⊃ r
   ∴ r

Exercise XXIV

8. p ⊃ (q ∨ r)
   ~q
   ~r
   ∴ ~p


9. (p ∨ q) ⊃ r
   ∴ p ⊃ r


10. (p & q) ⊃ r
    ∴ p ⊃ r


11. p ⊃ (q ⊃ r)
    ∴ (p & q) ⊃ r


12. (p & q) ⊃ r
    ∴ p ⊃ (q ⊃ r)


13. p ⊃ (q ⊃ r)
    q
    ~r
    ∴ ~p


14. p ⊃ (q ⊃ r)
    p ⊃ q
    ∴ r

(continued)

97364_ch06_ptg01_111-150.indd 141 15/11/13 10:15 AM

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