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 ↔ (¬b ∧ ¬a)11100100

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

¬b ↔ (¬b ∧ ¬a)
  1. 1a = 1, b = 1
  2. 2a = 1, b = 0
  3. 3a = 0, b = 1
  4. 4a = 0, b = 0
2.Easy

The complete truth table of ¬((¬a ∨ b) ∧ b) → (c ∧ ¬a) is written out. In how many rows N is b = 1 and c = 0?

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

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

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

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

q → p
  1. 1¬q → ¬p
  2. 2¬q ∧ p
  3. 3q ∧ ¬p
  4. 4¬q ∧ ¬p
5.Hard
qrr ∨ qr¬q11100100

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

r ∨ qr∴ ¬q
  1. 1q = 1, r = 1
  2. 2q = 1, r = 0
  3. 3q = 0, r = 1
  4. 4q = 0, r = 0
6.Hard

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

¬(((q → ¬p) ∨ r) → (¬p ∨ s))
N =

Answer key

  1. 1. a = 1, b = 0
  2. 2. N = 2
  3. 3. contradiction
  4. 4. q ∧ ¬p
  5. 5. q = 1, r = 1
  6. 6. N = 3

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