Solution 2.2 -《Sets, Functions, and Logic》

(1)
(a) 34159 is not a prime number.
(b) Not all roses are red or not all vialets are blue.
(c) If there are no hamburgers, I'll not have a hot dog.
(d) Fred won't go or he will play.
(e) The number x is positive and less than or equal to 10, or both negative and greater than 10.
(f) We will not win the first game and the second.

(2)
(a) T
(b) F
(c) F
(d) F
(e) T
(f) T

(3)
(c)(d)(f)

(4)
(f)

(5)
若mn是奇数，则m为奇数且n为奇数。
若mn为偶数，则必有mn被2整除，而m和n都不能被2整除，故mn不能被2整除，故mn为奇数。

(6)
若m,n为偶数，则mn能被2整除，故成立。

(7)

\(\phi\)	\(\psi\)	\(\urcorner\phi\)	\(\urcorner\psi\)	\(\phi\Rightarrow\psi\)	\(\urcorner\phi\Rightarrow\urcorner\psi\)
T	T	F	F	T	T
T	F	F	T	F	F
F	T	F	F	T	F
F	F	T	T	T	T

由真值表，可知\((\phi\Leftrightarrow\psi)\Leftrightarrow(\urcorner\phi\Rightarrow\urcorner\psi)\)

(8)
\((6)\Leftrightarrow(5)\)，则(6)和(5)的真值必相同，一方正确另一方必正确。