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 ↔ ¬(q → p)11?10?01?00?

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

q ↔ ¬(q → p)
N =
2.Easy
pqq → ¬p11?10?01?00?

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

q → ¬p
N =
3.Medium
¬r → ¬p¬p ∧ ¬r¬p → ¬rp → r

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

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

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

(p → q) ↔ (q → p)
  1. 1tautology
  2. 2contradiction
  3. 3contingency
5.Hard
∀x (P(x) → ¬Q(x))∀x (P(x) ∧ ¬Q(x))∃x (P(x) ∧ ¬Q(x))∃x (¬P(x) ∧ Q(x))

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

¬∀x (P(x) → Q(x))
  1. 1∀x (P(x) → ¬Q(x))
  2. 2∀x (P(x) ∧ ¬Q(x))
  3. 3∃x (P(x) ∧ ¬Q(x))
  4. 4∃x (¬P(x) ∧ Q(x))
6.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)

Answer key

  1. 1. N = 3
  2. 2. N = 3
  3. 3. ¬p → ¬r
  4. 4. contingency
  5. 5. ∃x (P(x) ∧ ¬Q(x))
  6. 6. ∃x ¬A(x)

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