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) ]

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