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
pq¬p ∨ q11100100

Exactly one row of the truth table makes ¬p ∨ q false. Click that row.

¬p ∨ q
  1. 1p = 1, q = 1
  2. 2p = 1, q = 0
  3. 3p = 0, q = 1
  4. 4p = 0, q = 0
2.Easy
pq¬q ∨ ¬p11100100

Exactly one row of the truth table makes ¬q ∨ ¬p false. Click that row.

¬q ∨ ¬p
  1. 1p = 1, q = 1
  2. 2p = 1, q = 0
  3. 3p = 0, q = 1
  4. 4p = 0, q = 0
3.Medium
¬b ∧ ab ∨ ¬a¬b ∨ a¬b → ¬a

Which formula is logically equivalent to b → a? Click it.

b → a
  1. 1¬b ∧ a
  2. 2b ∨ ¬a
  3. 3¬b ∨ a
  4. 4¬b → ¬a
4.Medium
tautologycontradictioncontingency

Is ¬(r ∨ ¬r) a tautology, a contradiction or a contingency? Click your answer.

¬(r ∨ ¬r)
  1. 1tautology
  2. 2contradiction
  3. 3contingency
5.Hard

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

((r → q) ∨ ¬s) → (p → (r ∧ p))
N =
6.Hard
c → b¬b → ¬cb ∧ cb → c

The premises b → a; a → c are given. Which conclusion follows from them? Click it.

b → aa → c
  1. 1c → b
  2. 2¬b → ¬c
  3. 3b ∧ c
  4. 4b → c

Answer key

  1. 1. p = 1, q = 0
  2. 2. p = 1, q = 1
  3. 3. ¬b ∨ a
  4. 4. contradiction
  5. 5. N = 12
  6. 6. b → c

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