propositional logic , writing the statement in terms of propositional variables I came across this question while practicing  propositional logic
Consider the argument: “If Anna can cancan or Kant can’t
cant, then Greville will cavil vilely. If Greville will cavil vilely, Will will want.
But Will won’t want. Therefore Kant can cant.” By writing the statement in
quotes as a proposition in terms of four propositional variables and simplifying,
show that it is a tautology and hence that the argument holds
I am not sure how to write the the proposition for both the sentences as one proposition.
please help me with this problem.
 A: you can change your vague phrase to this :

“If Anna can fight ,or Jhon can’t Betrayal, then Greville will saved.
  If Greville will saved, Alex will die. But Alex won’t die. Therefore
  Jhon can Betrayal.”

A: Let's first write the sentences in propositional logic:
(1) Anna_cancan ∨ ¬ Kant_cant → cavil_Greville
(2) cavil_Greville → Will_want
Now we know for a fact that:
(3) ¬ Will_want
Based on the law of contraposition in logic, we know that each conditional statement is logically equivalent to its contrapositive. This means that we can rewrite (2) as:
(4) ¬ Will_want → ¬ cavil_Greville
Since from (3) we know as a fact that "Will won't want", then based on (4) we can certify that "Greville will NOT cavil vilely" or ¬ cavil_Greville. So this becomes our fact:
(5) ¬ cavil_Greville
Using contraposition again and applying the De Morgan's law, we can rewrite (1) as:
(6) ¬ cavil_Greville → ¬ Anna_cancan ∧ Kant_cant
Because from (5) we already know the premise holds true, then the implication must be true:
(7) ¬ Anna_cancan ∧ Kant_cant
(7) means that "Anna can't cancan" and "Kant can cant" are both true statements and thus the conclusion (i.e "Kant can cant") is correct. 
