Discrete Mathematics
1.1.44
(c)q→¬r: If you miss the final examination, you won’t pass the course.
(d)p∨q ∨r: You have the flu, or you miss the final examination, or you
pass the course.
(a)x^2≥x means x(x-1)≥0,and all integers satisfy it. So there isn’t any
counterexample.
(b)If x=0,then x>0 and x<0 are both false. So x=0 is a counterexample.
(c)If x=0,then x≠0. So x=0 is a counterexample.
1.1.27
(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.
