This is a set theory problem associated to the pdf below htt

This is a set theory problem associated to the pdf below:

http://scholarworks.gvsu.edu/cgi/viewcontent.cgi?article=1007&context=books

2. Let P and Q are statements The election is decided and The votes have been counted, re- spectively. Express each of these compound statements as an English sentence. a) P, b) PVQ, c) PAQ, d) Q P, e)-P -Q.

Solution

let as given,

P = The election is decided

Q = The votes have been counted.

a) ¬P

¬ means not (yet)

hence we can say that

¬P = The election is not (yet) decided.

b) P Q

means or

so we can say that

P Q =  The election is decided or the votes have been counted

c) ¬P Q

¬ means not (yet)

means but with (write Q first)

hence we can say that

¬P Q = The votes have been counted but the election is not (yet) decided

d) Q P

means if condition from Q to P

so we can say that,

Q P = If the votes are counted then the election is decided

e) ¬P ¬Q

¬ means not (yet)

means if condition from P to Q

means with both side ¬ represented by unless

so we can say that,

¬P ¬Q = The votes have not been counted unless the election has been decided