Bai giai tri tue nhan tao tut4

TRƯỜNG ĐẠI HỌC BÁCH KHOA TP.HCM

Khoa Khoa học & Kỹ thuật Máy tính

TUTORIAL SESSION 4

PROPOSITIONAL LOGIC

1. Let p, q, and r be the following propositions:

p: You get an A on the final exam.

q: You do every exercise in the book.

r: You get an A in this class.

Write the following formulas using p, q, and r and logical connectives.

a. You get an A in this class, but you do not do every exercise in the book.

b. To get an A in this class, it is necessary for you to get an A on the final.

c. Getting an A on the final and doing every exercise in the book is sufficient for

getting an A in this class.

Solution:

a. r ˄ ¬q

b. r => p

c. p ˄ q => r

2. Is the sentences valid, unsatisfiable, or neither?

a. Smoke => Smoke

b. Smoke => Fire

c. ((Smoke  Heat) => Fire)  ((Smoke => Fire) ν (Heat => Fire))

Solution:

a. valid

b. neither

c. neither

3. Express sentences in propositional logic:

a. You can stay in dormitory only if you are an honor student or you are not a

graduate student.

b. You cannot pass the driver license exam if your knowledge exam’s score is under

60 unless you are older than 45 years old.

c. If the photo is digital or in black and white, then it is a portrait, else not.

d. If it is a portrait, then it is a picture of my friend.

Solution:

a. Symbolize the related predicates as follows: