CS 381 Solutions to Homework 2

Textbook pp. 11 - 13


2. (c) is a proposition, and it is false.

8 (a) $r \wedge \neg q$
(b) $p \wedge q \wedge r$
(c) $r \rightarrow p$
(d) $p \wedge \neg q \wedge r$
(e) $p \wedge q \rightarrow r$
(f) $r \leftrightarrow (q \vee p)$

20 (a) Converse: If I stay at home, then it will snow tonight.
Contrapositive: If I don't stay at home, it won't snow tonight.
(b) Converse: If I go to the beach, it is a sunny summer day.
Contrapositive: If I don't go to the beach, it is not a sunny summer day.
(c) Converse: If I sleep until noon, I stayed up late.
Contrapositive: If I don't sleep until noon, I did not stay up late.

21

p	q	$(p \vee \neg p)$	$(p \vee \neg q) \rightarrow q$	$(p \rightarrow q) \leftrightarrow (\neg q \rightarrow \neg p)$
F	F	T	F	T
F	T	T	T	T
T	F	T	F	T
T	T	T	T	T