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 ∧ (q → p))11100100

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

¬(q ∧ (q → p))
  1. 1p = 1, q = 1
  2. 2p = 1, q = 0
  3. 3p = 0, q = 1
  4. 4p = 0, q = 0
2.Easy
pq(p ↔ q) → q11100100

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

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

(r → p) ∧ (r ∧ ¬p)
  1. 1tautology
  2. 2contradiction
  3. 3contingency
4.Medium
abc¬((b ↔ c) ↔ a)c ∧ a¬((b ↔ c) ↔ a) → (c ∧ a)111?110?101?100?011?010?001?000?

In how many of the 8 rows of its truth table is ¬((b ↔ c) ↔ a) → (c ∧ a) true? Call this number N.

¬((b ↔ c) ↔ a) → (c ∧ a)
N =
5.Hard
∀x ¬A(x)∃x A(x)∃x ¬A(x)∀x A(x)

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

¬∀x A(x)
  1. 1∀x ¬A(x)
  2. 2∃x A(x)
  3. 3∃x ¬A(x)
  4. 4∀x A(x)
6.Hard
∀x P(x)∃x P(x)∃x ¬P(x)∀x ¬P(x)

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

¬∀x P(x)
  1. 1∀x P(x)
  2. 2∃x P(x)
  3. 3∃x ¬P(x)
  4. 4∀x ¬P(x)

Answer key

  1. 1. p = 1, q = 1
  2. 2. p = 0, q = 0
  3. 3. contradiction
  4. 4. N = 5
  5. 5. ∃x ¬A(x)
  6. 6. ∃x ¬P(x)

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