# How To Prove It – Exercise 1.1.1

Oct 07 2012

Solutions to Exercises in chapter 1 – Sentential Logic – of How To Prove It by Daniel J Velleman.

Problem (1): Analyze the logical form of the following statements:

(a) We’ll have either a reading assignment or homework problems, but we won’t have both homework problems and a test.

(b) You won’t go skiing, or you will and there won’t be any snow.

(c) $\sqrt 7 \nleq 2$

Solutions:

(a) $(P \vee Q) \wedge \neg (Q \wedge R)$, where:

P stands for “we’ll have a reading assignment”
Q stands for “we’ll have homework problems”, and
R stands for “we’ll have a test”.

(b) $\neg S \vee (S \wedge \neg N)$, where:

S stands for “you will go skiing”, and
N stands for “there will be snow”

(c) $\neg [ (\sqrt 7 < 2) \vee (\sqrt 7 = 2) ]$