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) ∧ (p ↔ ¬q))11100100

Exactly one row of the truth table makes ¬((q → p) ∧ (p ↔ ¬q)) false. Click that row.

¬((q → p) ∧ (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 ∧ p) ↔ ¬p11100100

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

(q ∧ p) ↔ ¬p
  1. 1p = 1, q = 1
  2. 2p = 1, q = 0
  3. 3p = 0, q = 1
  4. 4p = 0, q = 0
3.Medium
tautologycontradictioncontingency

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

((r → q) ∧ (q → p)) → (r → p)
  1. 1tautology
  2. 2contradiction
  3. 3contingency
4.Medium
r → ¬p¬r ∨ ¬pr ∧ ¬p¬r ∧ p

Which formula is logically equivalent to ¬(r → p)? Click it.

¬(r → p)
  1. 1r → ¬p
  2. 2¬r ∨ ¬p
  3. 3r ∧ ¬p
  4. 4¬r ∧ p
5.Hard
qp ∧ r¬qp

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

p ∨ rp → qr → q
  1. 1q
  2. 2p ∧ r
  3. 3¬q
  4. 4p
6.Hard
pqrq → (r ∨ p)qr111110101100011010001000

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

q → (r ∨ p)q∴ r
  1. 1p = 1, q = 1, r = 1
  2. 2p = 1, q = 1, r = 0
  3. 3p = 1, q = 0, r = 1
  4. 4p = 1, q = 0, r = 0
  5. 5p = 0, q = 1, r = 1
  6. 6p = 0, q = 1, r = 0
  7. 7p = 0, q = 0, r = 1
  8. 8p = 0, q = 0, r = 0

Answer key

  1. 1. p = 1, q = 0
  2. 2. p = 1, q = 0
  3. 3. tautology
  4. 4. r ∧ ¬p
  5. 5. q
  6. 6. p = 1, q = 1, r = 0

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