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) ∨ (¬q → p)11100100

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

(¬q ∧ p) ∨ (¬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(¬q → p) ∨ p11?10?01?00?

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

(¬q → p) ∨ p
N =
3.Medium
(r → p) ∧ (q → p)(r → q) → pr → (q → p)r ∧ (q → p)

Which formula is logically equivalent to (r ∧ q) → p? Click it.

(r ∧ q) → p
  1. 1(r → p) ∧ (q → p)
  2. 2(r → q) → p
  3. 3r → (q → p)
  4. 4r ∧ (q → p)
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
r ∧ ¬p¬rrp

The premises (q ∧ r) → p; q; ¬p are given. Which conclusion follows from them? Click it.

(q ∧ r) → pq¬p
  1. 1r ∧ ¬p
  2. 2¬r
  3. 3r
  4. 4p
6.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)

Answer key

  1. 1. p = 0, q = 0
  2. 2. N = 3
  3. 3. r → (q → p)
  4. 4. contradiction
  5. 5. ¬r
  6. 6. ∀x ∃y ¬R(x, y)

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