Try It Now

Exercises

1. Let d = "I like discrete structures", c = "I will pass this course" and s = "I will do my assignments". Express each of the following propositions in symbolic form:
   1. I like discrete structures and I will pass this course.
   2. I will do my assignments or I will not pass this course.
   3. It is not true that I both like discrete structures, and will do my assignments.
   4. I will not do my assignment and I will not pass this course.
      
      
3. Let p ="2 ≤ 5", q = "8 is an even integer", and r = "11 is a prime number". Express the following as a statement in English and determine whether the statement is true or false:
   
   1. ¬p ∧ q
   2. p → q
   3. (p ∧ q) → r
   4. p → (q ∨ (¬r))
   5. p → ((¬q) ∨ (¬r))
   6. (¬q) → (¬p)

Source: Al Doerr and Ken Levasseur, http://faculty.uml.edu/klevasseur/ads-latex/ads.pdf
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.

Solutions

1. Answer:
   
   1. d ∧ c 
   2. s ∨ ¬c
   3. ¬(d ∧ s)
   4. ¬s ∧ ¬c
      
      
3. Answer:
   
   1. 2 > 5 and 8 is an even integer. False.
   2. If 2 ⩽ 5 then 8 is an even integer. True.
   3. If 2 ⩽ 5 and 8 is an even integer then 11 is a prime number. True.
   4. If 2 ⩽ 5 then either 8 is an even integer or 11 is not a prime number. True.
   5. If 2 ⩽ 5 then either 8 is an odd integer or 11 is not a prime number. False.
   6. If 8 is not an even integer then 2 > 5. True.