Discrete Math Assignment #2 Evens Solution - 6:30PM

Introduction

Below is the solutions to the even problems for assignment #2...

1.2: 42:

1.3 2:

p	p'	(p')'
T	F	F' = T
F	T	T' = F

4a:

p	q	r	(p or q) or r	p or (q or r)
T	T	T	(T or T) or T = T	T or (T or T) = T
T	T	F	(T or T) or F = T	T or (T or F) = T
T	F	T	(T or F) or T = T	T or (F or T) = T
T	F	F	(T or F) or F = T	T or (F or F) = T
F	T	T	(F or T) or T = T	F or (T or T) = T
F	T	F	(F or T) or F = T	F or (T or F) = T
F	F	T	(F or F) or T = T	F or (F or T) = T
F	F	F	(F or F) or F = F	F or (F or F) = F

4b:

p	q	r	(p and q) and r	p and (q and r)
T	T	T	(T and T) and T = T	T and (T and T) = T
T	T	F	(T and T) and F = F	T and (T and F) = F
T	F	T	(T and F) and T = F	T and (F and T) = F
T	F	F	(T and F) and F = F	T and (F and F) = F
F	T	T	(F and T) and T = F	F and (T and T) = F
F	T	F	(F and T) and F = F	F and (T and F) = F
F	F	T	(F and F) and T = F	F and (F and T) = F
F	F	F	(F and F) and F = F	F and (F and F) = F

10a:

p	q	[p' & (p | q)] -> q
T	T	T
T	F	T
F	T	T
F	F	T

10b:

p	q	r	[(p -> q) & (q -> r)] -> (p -> r)
T	T	T	T
T	T	F	T
T	F	T	T
T	F	F	T
F	T	T	T
F	T	F	T
F	F	T	T
F	F	F	T

10c:

p	q	[p & (p -> q)] -> q
T	T	T
T	F	T
F	T	T
F	F	T

10d:

p	q	r	[(p | q) & (p -> r) & (q -> r)] -> r
T	T	T	T
T	T	F	T
T	F	T	T
T	F	F	T
F	T	T	T
F	T	F	T
F	F	T	T
F	F	F	T

1.4:

2a. True 2b. False 2c. False 2d. True

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