Discrete Mathematics
1. (¬Q(c) ∨P(c)) ∨R(c)/Commutative law from (7)
2. ¬Q(c) ∨(P(c)∨R(c))/Associative law from (8)
3. P(c) ∨(P(c)∨R(c))/Resolution from (3) and (9)
4. (P(c) ∨P(c)) ∨R(c)/ Associative law from (10)
5.P(c) ∨R(c)/Idempotent law from (11)
6.R(c) ∨P(c)/Commutative law from (12)
7. ¬R(c) →P(c)/ Logical equivalence from (13)
8. ∀x(¬R(x)→P(x))/Universal generalization from (14)
p ∴p∨q (Addition)
(e)p: I work all night on this homework, q: I can answer all the
exercises,r:I will understand the material
p→q, q→r ∴p→r (Hypothetical syllogism)
1.6.4
(a)p: Kangaroos live in Australia, q: Kangaroos are marsupials.
p∧q ∴q (Simplification)
(b)p: It is hotter than 100 degrees today, q : The pollution is dangerous.
p∨q, ¬p ∴q (Disjunctive syllogism)
(c)p: Linda is an excellent swimmer, q: Linda can work as a lifeguard.
p, p→q ∴q (Modus ponens)
(d)p: Steve will work at a computer company this summer, q: Steve will
be a beach bum.
