consequently.org: Logic Text Chapter 5 Solutions

Chapter 5: Vagueness and Bivalence

Question {5.1}

I will write ’ n ’ for ‘1/2’ as it’s smaller here. You can read it as “neither true nor false”. Each of the following are not L3 tautologies:

p	∨	~	p
n	n	n	n

~	(p	&	~	p)
n	n	n	n	n

(p	&	(p	⊃	q))	⊃	q
n	n	n	n	0	n	0

(p	⊃	~	p)	⊃	~	p
n	1	n	n	n	n	n

(p	&	~	p)	⊃	q
n	n	n	n	n	0

((p	⊃	q)	⊃	p)	⊃	p
n	n	0	1	n	n	n

All of the other formulas are tautologies.