Chapter 1: Deductive Reasoning and Logical Connectives

Question:
1.  Analyze the logical forms 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} \nleq2 $

Answer:
R = We have a reading assignment.
Q = We have a homework assignment
R = We have a test

 2. Analyze the logical forms 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 or 6,9, and 15.

 3. Analyze the logical forms of the following statements:
(a) Alice and Bob are not both in the room.
(b) Alice and Bob are both not in the room.
(c) Either Alice or Bob is not in the room.
(d) Neither Alice nor Bob is in the room.

 5. Let P stand for the statement "I will buy the pants" and S for the statement "I will buy the shirt.". What English sentences are represented by the following expressions.

(a) $\neg (P \wedge \neg S)$
(b) $\neg P \wedge \neg S$
(c) $\neg P \vee \neg S$