Kenneth Rosen Edition 6th Exercise 1.1 Question 6 (Page No. 17)

Question

Let p and q be the propositions “The election is decided” and “The votes have been counted,” respectively. Express each of these compound propositions as an English sentence.

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

Answer 1

A. The election is not decided

B. The election is decided or the votes have been counted

C. The election is not decided and the votes have been counted

D. If the votes have been counted then the election is decided

E. If the votes have not been counted then the election is not decided

F. If the election is not decided then the votes have not been counted

G. The election is decided if and only if the votes have been counted

F. The votes have not been counted or, the election is not decided and the votes have been counted.

Comments

@Deepak Poonia I think there is one more possible proposition for 'h'.

If the votes have been counted  then the election is not decided but the votes have been counted.