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
ab¬(¬b → ¬(a ↔ b))11100100

Exactly one row of the truth table makes ¬(¬b → ¬(a ↔ b)) true. Click that row.

¬(¬b → ¬(a ↔ b))
  1. 1a = 1, b = 1
  2. 2a = 1, b = 0
  3. 3a = 0, b = 1
  4. 4a = 0, b = 0
2.Easy
ab¬(¬b ↔ a) ∧ (b ∧ a)11?10?01?00?

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

¬(¬b ↔ a) ∧ (b ∧ a)
N =
3.Medium
¬(r ∨ p) ∧ ¬q¬(r ∨ p) ∧ q¬(r ∨ p) → ¬q(r ∨ p) ∧ ¬q

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

(r ∨ p) → q
  1. 1¬(r ∨ p) ∧ ¬q
  2. 2¬(r ∨ p) ∧ q
  3. 3¬(r ∨ p) → ¬q
  4. 4(r ∨ p) ∧ ¬q
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
∃x ∀y ¬R(x, y)∀x ∀y ¬R(x, y)∃x ∃y ¬R(x, y)∀x ∃y ¬R(x, y)

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

¬∃x ∀y R(x, y)
  1. 1∃x ∀y ¬R(x, y)
  2. 2∀x ∀y ¬R(x, y)
  3. 3∃x ∃y ¬R(x, y)
  4. 4∀x ∃y ¬R(x, y)
6.Hard

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

((s ↔ ¬p) → ¬q) ∧ (¬q ∨ (p ∨ r))
N =

Answer key

  1. 1. a = 0, b = 0
  2. 2. N = 1
  3. 3. (r ∨ p) ∧ ¬q
  4. 4. contradiction
  5. 5. ∀x ∃y ¬R(x, y)
  6. 6. N = 11

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