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
pqp ∧ q11?10?01?00?

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

p ∧ q
N =
2.Easy
aba → (¬a ∧ ¬b)11?10?01?00?

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

a → (¬a ∧ ¬b)
N =
3.Medium
tautologycontradictioncontingency

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

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

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

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

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

((r ∧ q) → ¬s) ∨ (s ∧ (¬q ∨ p))
N =
6.Hard
q ∧ pr ∨ p¬qq ∨ p

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

r ∨ q¬r ∨ p
  1. 1q ∧ p
  2. 2r ∨ p
  3. 3¬q
  4. 4q ∨ p

Answer key

  1. 1. N = 1
  2. 2. N = 2
  3. 3. contradiction
  4. 4. (q ∨ r) ∧ ¬p
  5. 5. N = 15
  6. 6. q ∨ p

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