self doubt

Question

how to write if and only if symbolic form explain in detail????

Answer 1

Lets say;

P: You’ll love new horror movie

q: you’re afraid of haunted house

r: you will find it very entertaining

so, expression will be : p if and only if q or r

we can break down above exp. into  p if q and p only if q

therefore, p if q : q→p

                  p only if q: p→q

finally symbolic form will be, 

(q→p) ∧ (p→q) v ¬r  by minimizing it,

(¬q v p) ∧ (¬p v q) v ¬r

(¬p¬q v pq) v ¬r this is equivalent to ;

(p ↔ q) v ¬r

Hence answer will be :

(p ↔ q) v ¬r

 

Comments

I think there’s typo in 5^th line, it should be: p if and only if q or ~r