Kenneth Rosen Edition 6th Exercise 1.1 Question 5 (Page No. 16)

Question

Let p and q be the propositions “Swimming at the New Jersey shore is allowed” and “Sharks have been spotted near the shore,” respectively. Express each of these compound propositions as an English sentence.

• A. $\neg q$
• B. $p \wedge q$
• C. $\neg p \vee q$
• D. $p \rightarrow \neg q$
• E. $\neg q \rightarrow p$
• F. $\neg p \rightarrow \neg q$
• G. $p \leftrightarrow \neg q$
• H. $\neg p \wedge (p \vee \neg q)$

Comments

A. Sharks have not been spotted near the shore.

B. Swimming at the New Jersey shore is allowed and sharks have been spotted near the shore.

C. If swimming at the New Jersey shore is not allowed then Sharks have been spotted near the shore.

D. If swimming at the New Jersey shore is allowed then Sharks have not been spotted near the shore.

E. If sharks have not been spotted near the shore then swimming at the New Jersey shore is allowed.

F. If swimming at the New Jersey shore is not allowed then Sharks have not been spotted near the shore.

G. Swimming at the New Jersey shore is allowed if and only if sharks have not been spotted near the shore.

H. Swimming at the New Jersey shore is not allowed and swimming at the New Jersey shore is allowed or Sharks have not been spotted near the shore.

Answer 1

Sharks have not been spotted near the shore.

Swimming at the New Jersey shore is allowed and Sharks have been spotted near the shore.

if swimming at the New Jersey shore is allowed then Sharks have been spotted near the shore.

if swimming at the New Jersey shore is allowed then Sharks have not been spotted near the shore.

Sharks have not been spotted near the shore or Swimming at the New Jersey shore is allowed.

Comments

A.Sharks have not been spotted near the shore.

B.Swimming at new jersey shore is allowed and sharks have been spotted,

C.Either swimming at new jersey shore is not allowed or sharks have been spotted near the shore.

D.Sharks have not been spotted near the shore ONLY IF swimming is allowed at new jersey shore.

               or

If swimming is allowed then sharks have not been spotted.

E.(similarily as D.) If sharks are not been spotted then swimming is allowed.

F.if swimming is not allowed then sharks are not spotted.(SAVAGE! :-p).

G.Swimming is allowed if and only if sharks are not spotted.

H.Either swimming is allowed or sharks have not been spotted,AND Swimming is not allowed.

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@Deepak Poonia I think answer of D should be like,

Sharks have not been spotted near the shore IF swimming is allowed at new jersey shore.

Becoz $p \space ONLY IF\space q$ means $(p \rightarrow q)$.