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
aba → b11100100

Exactly one row of the truth table makes a → b false. Click that row.

a → b
  1. 1a = 1, b = 1
  2. 2a = 1, b = 0
  3. 3a = 0, b = 1
  4. 4a = 0, b = 0
2.Easy
pq(p ↔ q) ↔ (q ∨ p)11?10?01?00?

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

(p ↔ q) ↔ (q ∨ p)
N =
3.Medium
(p ∨ q) ∧ r(p ∧ q) ∨ (p ∧ r)p ∧ (q ∨ r)(p ∨ q) ∧ (p ∨ 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. 3p ∧ (q ∨ r)
  4. 4(p ∨ q) ∧ (p ∨ r)
4.Medium
¬¬p → ¬r¬¬p ∧ r¬¬p ∧ ¬r¬p ∧ ¬r

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

¬p → r
  1. 1¬¬p → ¬r
  2. 2¬¬p ∧ r
  3. 3¬¬p ∧ ¬r
  4. 4¬p ∧ ¬r
5.Hard
∀x (F(x) ∧ ¬G(x))∀x (¬F(x) → ¬G(x))∀x (F(x) → ¬G(x))∃x (F(x) ∧ ¬G(x))

Which statement is equivalent to ¬∃x (F(x) → G(x)), with the negation moved all the way inside? Click it.

¬∃x (F(x) → G(x))
  1. 1∀x (F(x) ∧ ¬G(x))
  2. 2∀x (¬F(x) → ¬G(x))
  3. 3∀x (F(x) → ¬G(x))
  4. 4∃x (F(x) ∧ ¬G(x))
6.Hard

How many of the 16 rows of the truth table make (¬d ↔ b) → ((d → a) ↔ (c ∧ a)) true? Call this number N.

(¬d ↔ b) → ((d → a) ↔ (c ∧ a))
N =

Answer key

  1. 1. a = 1, b = 0
  2. 2. N = 1
  3. 3. (p ∨ q) ∧ (p ∨ r)
  4. 4. ¬p ∧ ¬r
  5. 5. ∀x (F(x) ∧ ¬G(x))
  6. 6. N = 12

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