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

How many rows N does the complete truth table of (r ∨ q) → ¬((¬r ↔ q) ↔ ¬p) have?

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

Is ((c → a) ∧ (a → b)) → (c → b) a tautology, a contradiction or a contingency? Click your answer.

((c → a) ∧ (a → b)) → (c → b)
  1. 1tautology
  2. 2contradiction
  3. 3contingency
4.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
5.Hard

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

¬(((r → s) ∨ (r ∧ q)) → (q ∧ p))
N =
6.Hard
pqrp → (r ∨ q)pr111110101100011010001000

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

p → (r ∨ q)p∴ 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 = 0, q = 1
  2. 2. N = 8
  3. 3. tautology
  4. 4. tautology
  5. 5. N = 10
  6. 6. p = 1, q = 1, r = 0

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