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Express each of these system specifications using the propositions p \"The user

ID: 3662627 • Letter: E

Question

Express each of these system specifications using the propositions p "The user enters a valid password", q "Access is granted", and r "The user has paid the subscription fee" and logical connectives (including negation). "Access is granted whenever the user has paid the subscription fee and enters a valid password." "If the user has not entered a valid password but has paid the subscription fee, then access is granted." For each of the above specifications, also express its negation as a logically equivalent compound proposition without a - in front. For example, if the specification was p rightarrow q then its negation is logically equivalent to p microvector -q. Justify your answers.

Explanation / Answer

a) “But” means “and” : r ¬ p

b) The hypothesis is a conjunction: (¬ p r)q.

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