Determine if the overall truth value for the following compound propositions in which some values are...

 

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Determine if the overall truth value for the following compound propositions in which some values are unknown are true, false or undetermined using the inverted pyramid method. Consider A,B,C to be true, X,Y,Z as false, and p, q as unknown. 1. 1. X p Example Solution: False X P F.U 2. B F (qv C 3. (A B)>p 4. (X>p)=(q ~Y) 5. (p q)>(~X v~Y) 6. ~(pA) (Bvq) 7. (X p)=(qv~Y) 8. ~[(~X>p) (Avq)] 9. ~p [Av (Xv q)] 10. {(~p~q)>[(AX) v~Y]} v B 11. (Xv~A) = [(Y >X) v ~B] 12. [(p ~A) v (q>B)] ~(A B) 13. {~Xv [p (Xvq)}>[q ~(~Av~Y)] 14. {A>[p (Xv~B)]}={Y [(pvq) > C]} 15. [pvq Z)]v~[X>(~A~Y)] Determine if the overall truth value for the following compound propositions in which some values are unknown are true, false or undetermined using the inverted pyramid method. Consider A,B,C to be true, X,Y,Z as false, and p, q as unknown. 1. 1. X p Example Solution: False X P F.U 2. B F (qv C 3. (A B)>p 4. (X>p)=(q ~Y) 5. (p q)>(~X v~Y) 6. ~(pA) (Bvq) 7. (X p)=(qv~Y) 8. ~[(~X>p) (Avq)] 9. ~p [Av (Xv q)] 10. {(~p~q)>[(AX) v~Y]} v B 11. (Xv~A) = [(Y >X) v ~B] 12. [(p ~A) v (q>B)] ~(A B) 13. {~Xv [p (Xvq)}>[q ~(~Av~Y)] 14. {A>[p (Xv~B)]}={Y [(pvq) > C]} 15. [pvq Z)]v~[X>(~A~Y)]

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