Northeastern University

• CS 3800

• 1. [4 Points] (a) For which values of the variables p, q, r is the expression ¬p ∨ q ∨ ¬r false? Solution: p = r = T and q = F (b) For which values of the variables p, q, r, s is the expression ¬p ∧ q ∧ ¬r ∧ ¬s true? Solution: p = r = s = F and q = T 2. [8 Points] Which of the following conditional statements are true and why? (a) If February has 30 days, then 7 is an odd number. Solution: Statement is true as it has the form F→T (b) If January has 31 days, then 7 is an even number. Solution: Statement is false as it has the form T→F (c) If 7 is an odd number, then February does not have 30 days. Solution: Statement is true as it has the form T→T (d) If 7 is an even number, then January has exactly 28 days. Solution: Statement is true as it has the form F→F 3. [8 Points] In this problem, the domain is t