Assignment#5 Model Answer - WordPress.com · Assignment 5 - Artificial Intelligence lecture Model answer Princess Nora Bint Abdulrahman University Faculty of Computer and Information

Prepared by: TA. Latifa Alrashed

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NET201- Principles of Information & Technology Systems First Semester 1435/1436 H Assignment 5 - Artificial Intelligence lecture Model answer

Princess Nora Bint Abdulrahman University Faculty of Computer and Information Sciences Department of Networks and Telecommunications

Question 1: Using the symbols Has, Loves, Dog, and Cat for the predicates “has”, “loves”, ”is a dog”, and “is a cat” respectively, write the following sentences in predicate logic:

a. John has a cat. ∃𝒙 [𝑪𝒂𝒕(𝒙) ∧𝑯𝒂𝒔(𝑱𝒐𝒉𝒏,𝒙)]

b. John loves all cats. ∀𝒙 [𝑪𝒂𝒕(𝒙) → 𝑳𝒐𝒗𝒆𝒔(𝑱𝒐𝒉𝒏,𝒙)]

c. John loves Anne. 𝑳𝒐𝒗𝒆𝒔(𝑱𝒐𝒉𝒏,𝑨𝒏𝒏𝒆)

d. Anne loves some dogs. ∃𝒙 [𝑫𝒐𝒈 𝒙 ∧ 𝑳𝒐𝒗𝒆𝒔(𝑨𝒏𝒏𝒆,𝒙)]

e. Not everything John loves is a cat. ∃𝒙 [𝑳𝒐𝒗𝒆𝒔 𝑱𝒐𝒉𝒏,𝒙 ∧ ¬𝑪𝒂𝒕(𝒙)]

Or ¬∀𝒙 [𝑳𝒐𝒗𝒆𝒔(𝑱𝒐𝒉𝒏,𝒙) → 𝒄𝒂𝒕(𝒙)]

f. Anne does not like some cats.

∃𝒙 [𝑪𝒂𝒕(𝒙) ∧ ¬ 𝐋𝐨𝐯𝐞𝐬(𝐀𝐧𝐧𝐞, 𝐱) ] g. If John loves a cat, Anne loves it.

∀𝒙 [ 𝑪𝒂𝒕 𝒙 ∧ 𝐋𝐨𝐯𝐞𝐬 𝐉𝐨𝐡𝐧, 𝐱 → 𝑳𝒐𝒗𝒆𝒔 𝑨𝒏𝒏𝒆,𝒙 ] h. John loves a cat if and only if Anne loves it.

∀𝒙 [ 𝑪𝒂𝒕 𝒙 ∧ 𝐋𝐨𝐯𝐞𝐬 𝐉𝐨𝐡𝐧, 𝐱 ↔ 𝑳𝒐𝒗𝒆𝒔 𝑨𝒏𝒏𝒆,𝒙 ] i. If John doesn’t like a cat, Anne loves it.

∀𝒙 [ 𝑪𝒂𝒕 𝒙 ∧ ¬ 𝐋𝐨𝐯𝐞𝐬 𝐉𝐨𝐡𝐧, 𝐱 → 𝑳𝒐𝒗𝒆𝒔 𝑨𝒏𝒏𝒆,𝒙 ]

Question 2: write the following sentences in predicate logic:

1. All mammals have hair.

∀𝒙 [𝑴𝒂𝒎𝒎𝒂𝒍(𝒙) → 𝑯𝒂𝒔(𝒙,𝒉𝒂𝒊𝒓)]

2. All rational numbers are natural numbers.

∀𝒙 [𝒓𝒂𝒕𝒊𝒐𝒏𝒂𝒍(𝒙) → 𝒏𝒂𝒕𝒖𝒓𝒂𝒍(𝒙)]

3. There exists a MATH 218 student who has tried out for American Idol.

∃𝒙 [𝒔𝒕𝒖𝒅𝒆𝒏𝒕 𝒙 ∧ 𝑻𝒓𝒚(𝒙,𝑨𝒎𝒆𝒓𝒊𝒄𝒂𝒏 𝑰𝒅𝒐𝒍)]

4. There exists a real number whose square is not positive.

∃𝒙 [𝒓𝒆𝒂𝒍 𝒙 ∧ 𝒔𝒒𝒖𝒂𝒓𝒆 (𝒙 ,¬ 𝒑𝒐𝒔𝒊𝒕𝒊𝒗𝒆 𝒙 )]


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5. Every person in New Britain has seen a movie starring William Shatner.

∀𝒙 [𝑩𝒓𝒊𝒕𝒊𝒔𝒉𝑷𝒆𝒓𝒔𝒐𝒏 𝒙 → 𝒔𝒆𝒆(𝒙, 𝒔𝒂𝒓𝒓𝒊𝒏𝒈(𝑾𝒊𝒍𝒍𝒊𝒂𝒎 𝑺𝒉𝒂𝒕𝒏𝒆𝒓,𝒎𝒐𝒗𝒊𝒆)]

Question 3: Let P(x), Q(x), and R(x) be the following predicates, all with domain (set) {students in this 218 class}.

P(x): x was born in the United States.

Q(x): x speaks more than one language.

R(x): x has a passport.

Translate the following into fluid English sentences that demonstrate understanding:

1. ∀x[Q(x) ∨ ￢R(x)]

For all students in this 218 class speak more than one language or don’t have a

passport

2. ∃x[￢P(x) ∧ (Q(x) ∨ R(x))]

There is a student in this 218 class who wasn’t born in the United States and either

speaks more than one language or has a passport.

3. ∀x(R(x) → (P(x) ∧ Q(x)).

For all students in this 218 class who have a passport were born in the United

States and speak more than one language.

Now translate the following statements into quantifier form:

1. “There is a student in this 218 class who wasn’t born in the U.S. and speaks more

than one language, but doesn’t have a passport.”

∃x [￢P(x) ∧ (Q(x) ∧ ￢R(x))]

2. “No one in this 218 class was both born abroad and speaks more than one

language.”

￢∃x [￢P(x) ∧ Q(x)]


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3. “No one in this 218 class who was born abroad speaks more than one language.”

∀x [￢P(x) → ￢Q(x)]

Question 4: By using the Breadth First Search technique. Find the node (L) from the following graph. (Note: consider the DOUBLE-LINED arrows and ignore the SINGLE-LINED arrows)

1. Convert the following graph into a tree (consider node (A) to be the root).

2. Determine the required path to find node (L).


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1. Convert the following graph into a tree (consider node (A) to be the root).

A

B F

D M

N

O

P Q

E

H

I G

L

K

J

C


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Question 5: By using the Depth First Search technique. Find the node (L) from the graph below. (Note: consider the DOUBLE-LINED arrows and ignore the SINGLE-LINED arrows)

1. Use the tree that you already have drawn.


A

B F

D M

N

O

P Q

E

H

I G

L

K

J

C


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Question 6: Apply the two previous searching techniques (BFS) and (DFS) to find node (P) and determine the path and number of movements for each.

a. BFS Path to find node ( P )

A

B F

D M

N

O

P Q

E

H

I G

L

K

J

C The search path AFC comes to a dead end, so we backtrack to A and continue the search along the path ABMEHGL, which comes to a goal

The path to find node (L) using the DFS technique:

A B M E H G L


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A

B F

D M

N

O

P Q

E

H

I G

L

K

J

C

The path to find node (P) using the BFS technique:

A F B C M D E N H O G I Q P


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b. DFS Path to find node ( P )

A

B F

D M

N

O

P Q

E

H

I G

L

K

J

C

The search path AFC comes to a dead end, so we backtrack to A and continue the search along the path ABMEHGLkJ, which also comes to a dead end.

Backtracking to node H and search along the path ABMEHI, results in another dead end.

Backtracking to node B and search along the path ABDNOQ, results in another dead end.

Backtracking to node O and search along the path ABDNOP, we hit the goal

The path to find node (E) using the DFS technique:

A B D N O P

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Assignment#5 Model Answer - WordPress.com · Assignment 5 - Artificial Intelligence lecture Model answer Princess Nora Bint Abdulrahman University Faculty of Computer and Information