Question

Nigel Rex, Remski Catsakoff and Rudolfo, are back with another logic problem. Using the variables as indicated below, translate the following English sentences into propositions and then provide a formal proof to show the conclusion: Nigel does not play with Rudolfo. Remski is calm or Rudy is not thin. If Nigel is not short or Rudolfo is thin, then Rudolfo dislikes corn. If Nigel is short then he plays with Rudolfo. If Nigel is not short or Rudolfo dislikes corn then Remski is not calm. Use a formal argument to show that Rudolfo is not thin.

variable means

16. p Nigel is short

17. q Rudolfo is thin

18. r Rudolfo dislikes corn

19. s Remski is calm

20. t Nigel plays with Rudolfo

Answer 1

Solution:

Nigel does not play with rudolfo : ~ t

remski is calm or rudy is not thin : s v ~ q

If nigel is not short or rudy is thin then,rudy dislikes corn : (~p v q) r

If nigel is not short then he plays with rudolfo : p t

If nigel is not short or rudolfo dislike corn,then remski not calm: ( ~ p v r) ~ s

Show: ~ q is true

Since p t is true

~ t is true

Using modus tollence p t is true, ~ t is true

so ~ p is true

So (~ p v q ) r , ~ p is true

So using modus rones r is true

similarly (~ p v r ) s.~p is true

so using modus pones ~s is true

so we have ~s is true, s v ~q is true

using disjuctive syllogism ~ q is true