I am a newbie to Stack-Exchange and if there is any problem in my question -- I apologize beforehand .
I was working my way through some Propositional Logic Questions in Discrete Maths by Rosen , when I came across the following question :
Let p, q, and r be three propositions
p : Grizzly bears have been seen in the area
q : Hiking is safe on the trail.
r : Berries are ripe along the trail.
Write the propositions using p, q, and r and logical connectives (including negations):
For hiking on the trail to be safe, it is necessary but not sufficient that berries not >be ripe along the trail and for grizzly bears not to have been seen in the area
My Solution :
q => (~r AND ~p) -- because (~r AND ~p) is the necessary condition
Book's Solution :
(q => (~r AND ~p) ) AND ~((~r AND ~p) => q)
I am puzzled why the book's solution is as it is given .
Can someone help me out ? Would be grateful .