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
pqq ∨ (¬p ↔ q)11?10?01?00?

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

q ∨ (¬p ↔ q)
N =
2.Easy
pqr¬(q ∧ (¬r → ¬p))111?110?101?100?011?010?001?000?

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

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

Which formula is logically equivalent to r → q? Click it.

r → q
  1. 1¬r → ¬q
  2. 2¬q ∧ ¬r
  3. 3¬q → ¬r
  4. 4q → r
4.Medium
tautologycontradictioncontingency

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

¬((r ∧ p) → r)
  1. 1tautology
  2. 2contradiction
  3. 3contingency
5.Hard
∃x (F(x) ∧ ¬G(x))∀x (F(x) → ¬G(x))∀x (¬F(x) → ¬G(x))∀x (F(x) ∧ ¬G(x))

Which statement is equivalent to ¬∃x (F(x) → G(x)), with the negation moved all the way inside? Click it.

¬∃x (F(x) → G(x))
  1. 1∃x (F(x) ∧ ¬G(x))
  2. 2∀x (F(x) → ¬G(x))
  3. 3∀x (¬F(x) → ¬G(x))
  4. 4∀x (F(x) ∧ ¬G(x))
6.Hard
∀x F(x)∃x F(x)∃x ¬F(x)∀x ¬F(x)

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

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

Answer key

  1. 1. N = 3
  2. 2. N = 5
  3. 3. ¬q → ¬r
  4. 4. contradiction
  5. 5. ∀x (F(x) ∧ ¬G(x))
  6. 6. ∃x ¬F(x)

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