Suppose you are reading a ctional universitys password policy, and it says: You can access university Wi-Fi with your phone or your computer by connecting using your university password. You have to change your password after 6 months. For your security, you will be locked out of your account at any time when multiple failed attempts to reconnect are detected. You know that if your phone cannot connect to Wi-Fi, it will make multiple failed attempts to reconnect. Similarly, if your computer cannot connect to Wi-Fi, will make multiple failed attempts to reconnect. Also, if you change the password, then for a few minutes until you update their Wi-Fi both your phone and your computer would not be able to connect to Wi-Fi. In this question, you need to nd out whether there is a way to avoid being locked out if you change your password. Let us name the propositions occurring in this problem as follows:

p: You changed the password

q: You are locked out of your account

r: Your phone can connect to Wi-Fi

s: Your computer can connect to Wi-Fi

t: There are multiple failed attempts to reconnect

(a) Convert the statements in the paragraph above (both the policy and your knowledge) into logic form using these variable names. For example, the last sentence would become p rs.

(b) Use natural deduction to see whether being locked out is unavoidable when you change your password, given these statements. Your proof should consist of several applications of modus ponens and/or transitivity rule (maybe converting to implication or taking a contrapositive of an implication rst), and potentially some auxiliary rules listed in the slides.

(c) Now use resolution to verify that your argument in the previous sub question is correct. Recall that to do that, you will need to write a negation of AND of premises implies conclusion (where premises are your formulas from part a)), convert all premises and negated conclusion into CNF form, and do a resolution refutation on the resulting formula