a) Define the following concept formally using description logics: A university has a female president, at least 5 vice presidents, all department chairs are professors whose ranks are full, and who have served the university for at least 10 years. b) Suppose we have a knowledge base -- PhD circle-equals [AND GraduateStudent [FILLS :Program doctorate]] -- GraduateStudent squared-subset-or-equals Student Which of the following two sentences is a valid one? Which one can only be entailed? A) [AND Student Male] squared-subset-or-equals Student B) [AND PhD Male] squared-subset-or-equals Student

Question For each of the following, determine whether argument is valid. You may use a counterexample or equivalence transformations to justify your answer. (a) P→ q (b) (c) קר :: 79 P→r q→r ¬(pv q) :: r P→r q→r qV¬r :: 19

(b) Let C(x, y) mean that "student x has taken course y", where the domain for x consists of all students at your school and the domain for y consists of all courses offered at the university. Express each of these sentences in terms of C(x, y), quantifiers, and logical connectives. (i) Not every student has taken the course SWEN2002. (ii) Laila has taken every course except for SWEN3000. (iii)Kayley has taken exactly one course. (c) Write each of the following statements in the form if p, then q. (i) Shane has an allergy whenever he eats peanuts. (ii) It is necessary to have studied abroad to have the full experience of university. (iii)Rich will yell unless the children do not walk on his lawn. (d) Given the hypotheses, mk and (-h A-k)→ -p, m A p show that-h→m is a valid conclusion.

Mathematical Logic First-order or predicate logic. Show that the sum relation, {(m,n,p)|p=m+n}, is not definable on (N; ∙). Hint: Consider an automorphism of (N; ∙) that interchanges two primes. Where N is the set of natural numbers. Please be as clear as possible. Show and explain all the steps. Thank you very much.

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Answer question no 4 and 5 only. please answer with proper explanation and step by step solution.

Question 5 How do you model the following situation with a use case diagram: Mother and daughter cook dinner together. Sometimes it is necessary that one of them gets chives from the garden. B D 옷차 mother daughter (abstract) both mother OK K+K daughter mother daughter K mother daughter get chives get chives extend get chives get chives cook cook extend extend» cook cook «extend