· web viewwrite each of the following english sentences in propositional logic: it’s....

Princess Nora Bint Abdulrahman University NET201- Principles of Information & Technology Systems Faculty of Computer and Information Sciences Second Semester 1437/1438 HDepartment of Information Technology Tutorial 5 – Artificial Intelligence

Q1): Represent the following as a semantic network:

We consider any individual studying or conducting research at a university to be an academic. Within the academic community, there are two categories: students and staff.

Students get some form of funding and staff get a salary. Students who are studying for their primary degree are called undergraduates, and attend a particular course (e.g. Mathematics, Computer Science, Geography, etc.). All other students are called post-graduates and have a primary degree. They also have some research area (e.g. Artificial Intelligence).

Three categories of staff exist: lecturers, demonstrators, and researchers. Lecturers give a course (e.g. C/C++ Programming), and demonstrators provide support for those courses. On the other hand, researchers conduct research into a particular research area.

John is a student studying Computer Science. Mary is a lecturer in Computer Science.

Q2): Represent the semantic network of Q1 as a set of frames.

Q3): Say whether each of the following is a syntactically legal sentence of Propositional Logic.

a. p ∧ ¬p legal b. ¬p ∨ ¬p legal

c. ¬ (q ∨ r) ¬q →¬¬p Not legal d. (p ∨ q) ∧ (r ∨ q) legal

e. (p →q) ¿ –( p ←q) Not legalf. (p ↔q) ¿ –( p →q) legal

g. (p ↔q) ¿ –(p →q) ∧ ( p ←q) legal


Q4): If the symbols C, W, and H mean “it is cold”, “it is warm”, and “it is hot”, write the English statements corresponding to the following statements in propositional logic:

a. ¬H “It is not hot”b. W ∨ H “it is warm or it is hot”c. W ∧ H “it is warm and hot”d. W ∧ (¬H ¿ “it is warm but it is not hot” e. ¬ (W ∧ H) “it is not true that it is warm and hot” or “it is neither warm nor

hot”f. W→H “if it is warm, then it is hot”g. (¬C) →W “if it is not cold, then it is warm”h. ¬ (W→H ) “it is not true that if it is warm, then it is hot”i. H→(¬W) “if it is hot, then it is not warm” or “it is not warm if it is hot”j. ((¬C)∧H ) ∨ (C ∧¿¬H ¿) “it is not cold and hot, or it is cold and not hot”

Q5): Using the symbol R for the sentence “It is raining” and the symbol S for the sentence “It is sunny”, write each of the following English sentences in propositional logic:

a. It is not raining. ¬ Rb. It is not sunny. ¬ Sc. It is neither raining nor sunny. ¬ (R ∧ S)d. It is raining and sunny. (R ∧ S)e. If it is sunny, then it is not raining. (S →(¬ R))


f. If it is raining, then it is not sunny. (R →(¬ S))g. It is sunny if and only if it is not raining. (S ↔(¬ R))h. It is not true that if it is not raining, it is sunny. ¬ ((¬R) → S)

Q6): Write each of the following English sentences in propositional logic:

a. It’s raining whenever I carry an umbrella. Using the symbol U for the statement “I carry an umbrella” and the symbol R for the statement “it’s raining”(U→R)

b. It is necessary for you to get a C- in MATH 218 to graduate. Using the symbol C for the statement “you get a C in math 218” and the symbol G for the statement “you will graduate”(C→G)

c. We never have class on Friday.Using the symbol F for the statement “it is Friday” and the symbol C for the statement “there are no classes”(F→¬C)

d. To get a promotion, you must work hard.Using the symbol H for the statement “you work hard” and the symbol P for the statement “you get a promotion”(H→P)

e. You can access the website only if you pay a subscription fee.Using the symbol P for the statement “you pay a subscription fee” and the symbol A for the statement “you access the website”(P→A)

Q7): Use a truth table to find whether the following argument is valid:

{P∨Q ,P }∨– Q


Here row 3 and row 4 need to be checked. Although row 4 is ok, row 3 shows a counterexample (two true premises result in false conclusion). The argument is therefore invalid.

Q8): Use a truth table to find whether the following argument is valid:

{P→Q ,Q→R }∨– (P→R)

Here row 1, 2, 4, and 8 need to be checked. These rows do not show a counterexample, so the argument is valid.

· web viewwrite each of the following english sentences in propositional logic: it’s....

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