Use the truth table method to investigate the following questions. You must tell me whether the indicated entailment holds or not and you must justify your answer using a truth table. Does ((pq) Aq) entail -p? Does (pAq) entail (p Vq)? Does (pq) entail (q> p)? Question 2 (5pts) For question (2), assume we have the following translations from English to propo- sitional logic. p Yukiko is a linguist q=Christine is a lawyer Pavlos is a logician Now translate the following English sentences into propositional logic. Some of these sentences might have multiple translations. If you feel like it's ambiguous, note it, and just give one translation. If Pavlos is a logician then Yukiko is a linguist. Christine is a lawyer and if Yukiko is a linguist then it's not the case that Pavlos is a logician. It's not the case that if Pavlos is a logician then Yukiko is a linguist. Yukiko is a linguist or Pavlos is a logican and Christine is a lawyer. It is not the case that it is not the case that Christine is a lawyer. Question 3 (5pts) Using the same translations for the atomic sentences in question (2), now translate the following propositional logic sentences into English. (p Vr) ((pr)^(r> p)) (p > (q>r)) (p > (qvr)) (p^r) Question 4 (5pts) Consider the following pairs of English sentences. Check whether S entails S2 by translating the two sentences into propositional logic and then building the requisite truth table. Using the truth table as justification, make sure you tell me whether S entails S2. S: Yukiko is a linguist or Pavlos is a logician and it's not the case that Pavlos is a logician. S2 Yukiko is a linguist. S: Yukiko is a linguist and if Yukiko is a linguist then Pavlos is a logician. S2 Pavlos is a logician. S Yukiko is a linguist. S2 Pavlos is a logician or It's not the case that Pavlos is a logician.