Appendix B
Solutions to Exercises
These Things Take Time.
—The Smiths
Solutions: Chapter 2
[2.1] Which of the following are not legal WFF of PTL, and why?
(a) 
............................................not legal – left-hand side of ‘
’ is not a WFF
(b) 
........................................legal
(c) 
...............................not legal – binary operator expected between the propositional symbol ‘
’ and ‘(’
[2.2] How might we represent the following statements in PTL?
(a) “In the next moment in time, running’ will be true and, at some time after that, ‘
’ will be true.”.........
(b) “There is a moment in the future where either ‘
’ is always true, or ‘’ is true in the next moment in time. ...
