# How To Prove It – Exercise 1.1.2

Oct 07 2012

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

Problem (2): Analyze the logical form of the following statements:

(a) Either John and Bill are both telling the truth, or neither of them is.

(b) I’ll have either fish or chicken, but I won’t have both fish and mashed potatoes.

(c) 3 is a common divisor of 6, 9, and 15.

Solutions:

(a) $(J \wedge B) \vee (\neg J \wedge \neg B)$, where:

J stands for “John is telling the truth”, and
B stands for “Bill is telling the truth”.

(b) $(F \vee C) \wedge \neg (F \wedge P)$, where:

F stands for “I’ll have fish”,
C stands for “I’ll have chicken”, and
P stands for “I’ll have mashed potatoes”

(c) $(6 \mod 3 = 0) \wedge (9 \mod 3=0) \wedge (15 \mod 3=0)$

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