Propositional logic & proofs worksheet with answers

Free printable Propositional logic & proofs worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
abb ∨ (a ↔ ¬b)11?10?01?00?

Complete the truth table (1 = true, 0 = false). In how many rows N is b ∨ (a ↔ ¬b) true?

b ∨ (a ↔ ¬b)
N =
2.Easy
ab¬((¬a ∨ b) ∧ (¬b ∨ a))11?10?01?00?

Complete the truth table (1 = true, 0 = false). In how many rows N is ¬((¬a ∨ b) ∧ (¬b ∨ a)) true?

¬((¬a ∨ b) ∧ (¬b ∨ a))
N =
3.Medium
(q ∨ p) ∧ ¬r¬(q ∨ p) ∧ ¬r¬(q ∨ p) ∧ r¬(q ∨ p) → ¬r

You want to prove (q ∨ p) → r by contradiction. Which statement do you assume at the start? Click it.

(q ∨ p) → r
  1. 1(q ∨ p) ∧ ¬r
  2. 2¬(q ∨ p) ∧ ¬r
  3. 3¬(q ∨ p) ∧ r
  4. 4¬(q ∨ p) → ¬r
4.Medium
(p ∧ q) ∨ r(p ∨ q) ∧ (p ∨ r)(p ∧ q) ∨ (p ∧ r)p ∨ (q ∧ r)

Which formula is logically equivalent to p ∧ (q ∨ r)? Click it.

p ∧ (q ∨ r)
  1. 1(p ∧ q) ∨ r
  2. 2(p ∨ q) ∧ (p ∨ r)
  3. 3(p ∧ q) ∨ (p ∧ r)
  4. 4p ∨ (q ∧ r)
5.Hard
q ∧ rq → r¬q → ¬rr → q

The premises q → p; p → r are given. Which conclusion follows from them? Click it.

q → pp → r
  1. 1q ∧ r
  2. 2q → r
  3. 3¬q → ¬r
  4. 4r → q
6.Hard

How many of the 16 rows of the truth table make ((r ↔ q) ∧ (¬s → q)) ↔ (¬s ∧ (r ∧ p)) true? Call this number N.

((r ↔ q) ∧ (¬s → q)) ↔ (¬s ∧ (r ∧ p))
N =

Answer key

  1. 1. N = 3
  2. 2. N = 2
  3. 3. (q ∨ p) ∧ ¬r
  4. 4. (p ∧ q) ∨ (p ∧ r)
  5. 5. q → r
  6. 6. N = 10

Full step-by-step solutions: practise this topic on examproblems.com.