1) What is compositionality? Give a concise definition.
2) Assume that p and q represent the propositions 2+2 = 4 and 2+3 = 4,
respectively. Compute the truth values of the following propositions (Note that the first sentence
of this question is implicitly telling you the respective truth values of the propositions p and q).
(1) ¬p
(2) ¬(¬p)
(3) p ? ¬p
(4) p ? q
(5) ¬p ? q
(6) ¬(p ? q)
(7) ¬(¬p ? ¬q)
(8) ¬(p ? q)
(9) (p ? p) ? ¬q
(10) ¬p ? ¬(p ? q)
Note: In Question 2, you need to show your work. In other words, just saying "true" or "false"
as an answer is not enough.
3) Give definitions for the terms valid and invalid as they apply to what we call reasoning.
4) What is entailment? Give an example to illustrate your definition.