Q: Use truth tables to test the validity of the argument. p ? ~q q ? ~p/

? p ? q

A: Since a truth table would be so long, and you'd have to have a very wide
piece of paper to get it all in, [ I'd just take the four cases and work each
one out separately and see if we get T in every case:
Case p=T and q=T
[(p -> ~q) ^ (q -> ~p)] -> (p V q)
[(T -> ~T) ^ (T -> ~T)] -> (T V T)
[(T -> F ) ^ (T -> F)] -> T
[ F ^ F ] -> T
F -> T

T
Case p=T and q=F
[(p -> ~q) ^ (q -> ~p)] -> (p V q)
[(T -> ~F) ^ (F -> ~T)] -> (T V F)
[(T -> T ) ^ (F -> F) ] -> T
[ T ^ T ] -> T
T -> T
T
Case p=F and q=T
[(p -> ~q) ^ (q -> ~p)] -> (p V q)
[(F -> ~T) ^ (T -> ~F)] -> (F V T)
[(F -> F ) ^ (T -> F )] -> T
[ T ^ F ] -> F
F -> F
T
Case p=F and q=F
[(p -> ~q) ^ (q -> ~p)] -> (p V q)
[(F -> ~F) ^ (F -> ~F)] -> (F V F)
[(F -> T ) ^ (F -> T )] -> F
[ T ^ F ] -> F
F -> F
T
All four cases come out T, so the argument is valid.
]

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