Tutorial Problems 1 - For Week 2

From the text do:

Exercise 2.3.1, p. 21. 

    1a to 1e

    2b, 2c. 

 


 

For those of you who do not yet have the text the questions are the following. This is a service that will not continue past the 3rd week.

 

Exercise 2.3.1, p. 21:

 

1.       Show the following formulas to be S5-Valid.

 

a.        []p É

b.        <>p É []<>p

c.        [][](p É p)

d.        [](p É q) É []([]p É []q)

e.        <><>p É <>p

 

2.       Translate the following arguments into S5 and test for validity. Use only the dictionary provided..

 

b.        If it rains then moisture must be in the air. If moisture is in the air then the gauge will show a reading. Since the gauge shows no reading, it is not raining.

          [R = it is raining, M = moisture is in the air, G = the gauge shows a reading]

c.        If the object has mass then it must attract all other objects. Since there is an object other than itself which it does not attract, it must have no mass.

          [M = the object has mass, A = the object attracts all other objects]