From the text do:
Exercise 2.4.1, p. 26.
1b to 1f
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 2.4.1, p. 26:
1. Test the following formulas for S5-Validity.
Where necessary, unabbreviate the defined operators.
If any formula is not S5-Valid, provide a counter-example with a test to show that it is such
b. []<>p É <>[]p
c. []([]p É []q) v []([]q É []p)
d. (p É <>q) É (<>q É ~p) (skeptic's thesis)
e. (p É q) É ~<>(p & ~q)
f. (~<>p É [](p É q)) (a paradox of strict implication)