logic 101

FOR THE QUIZ, JUST WRITE THE SENTENCE FORMS FOR WHICH THE TWO SENTENCES BELOW ARE A SUBSTITUTION INSTANCE. You don't have to write out the sentence form--just the letter which precedes it.

USE THE FOLLOWING SENTENCES. (DO NOT USE ANY OF THE NUMBERED SENTENCES IN EXERCISE 3-4.) RUN EACH OF THE TWO SENTENCES BELOW THROUGH ALL OF THE SENTENCE FORMS ON THE RHS OF EXERCISE 3-4. LIST THE LETTERS FOR WHICH EACH OF THE TWO SENTENCES BELOW IS A SUBSTITUTION-INSTANCE. (---> means 'if ... then ...' It is the horseshoe. * means 'and.' It is the dot.

1. ~ ~ [ ( A v ~A) v ~ ~ B]

2. ~ ~A --> ~ (~ B --> C)

Answer Choices

a. p

b. 􏰂p

c. p∨q

d. p􏰀q e. 􏰂p∨q

f. 􏰂p􏰀q

g. 􏰂p􏰀􏰂q h. 􏰂(p∨q)

i. 􏰂(p􏰀q)

j. 􏰂(􏰂p􏰀q) k. (p∨q)􏰀r l. p∨(q􏰀r)

m. (􏰂p∨q)􏰀r n. 􏰂(p∨q)􏰀r o. (p∨q)􏰀􏰂r p. 􏰂[p∨(q􏰀r)] q. 􏰂[(p∨q)􏰀r]