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.

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1.Easy
pq¬(¬(¬q ∨ ¬p) → ¬(q ∨ p))11100100

Exactly one row of the truth table makes ¬(¬(¬q ∨ ¬p) → ¬(q ∨ p)) true. Click that row.

¬(¬(¬q ∨ ¬p) → ¬(q ∨ p))
  1. 1p = 1, q = 1
  2. 2p = 1, q = 0
  3. 3p = 0, q = 1
  4. 4p = 0, q = 0
2.Easy
pqq → ¬(q → p)11?10?01?00?

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

q → ¬(q → p)
N =
3.Medium
tautologycontradictioncontingency

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

(q ↔ r) ∧ (q ↔ ¬r)
  1. 1tautology
  2. 2contradiction
  3. 3contingency
4.Medium
tautologycontradictioncontingency

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

¬(a ∧ c) ↔ (¬a ∨ ¬c)
  1. 1tautology
  2. 2contradiction
  3. 3contingency
5.Hard
∃x (F(x) ∧ ∀y ¬R(x, y))∀x (F(x) ∧ ∀y ¬R(x, y))∃x (¬F(x) ∧ ∃y R(x, y))∃x (F(x) → ∀y ¬R(x, y))

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

¬∀x (F(x) → ∃y R(x, y))
  1. 1∃x (F(x) ∧ ∀y ¬R(x, y))
  2. 2∀x (F(x) ∧ ∀y ¬R(x, y))
  3. 3∃x (¬F(x) ∧ ∃y R(x, y))
  4. 4∃x (F(x) → ∀y ¬R(x, y))
6.Hard
pqp → q¬p¬q11100100

The argument with premises p → q; ¬p and conclusion ¬q is invalid. Click the row of the truth table that is a counterexample.

p → q¬p∴ ¬q
  1. 1p = 1, q = 1
  2. 2p = 1, q = 0
  3. 3p = 0, q = 1
  4. 4p = 0, q = 0

Answer key

  1. 1. p = 1, q = 1
  2. 2. N = 3
  3. 3. contradiction
  4. 4. tautology
  5. 5. ∃x (F(x) ∧ ∀y ¬R(x, y))
  6. 6. p = 0, q = 1

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