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

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

((¬b → ¬c) ∨ ¬b) → ¬(a → (¬c ∨ a))
N =
2.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
3.Medium
tautologycontradictioncontingency

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

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

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

(q → r) ↔ (r → q)
  1. 1tautology
  2. 2contradiction
  3. 3contingency
5.Hard

How many of the 16 rows of the truth table make (c ∧ (d ∧ b)) ∨ (¬c ∨ (d → a)) true? Call this number N.

(c ∧ (d ∧ b)) ∨ (¬c ∨ (d → a))
N =
6.Hard
∀x (¬A(x) → ¬B(x))∀x (A(x) → ¬B(x))∀x (A(x) ∧ ¬B(x))∃x (A(x) ∧ ¬B(x))

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

¬∃x (A(x) → B(x))
  1. 1∀x (¬A(x) → ¬B(x))
  2. 2∀x (A(x) → ¬B(x))
  3. 3∀x (A(x) ∧ ¬B(x))
  4. 4∃x (A(x) ∧ ¬B(x))

Answer key

  1. 1. N = 2
  2. 2. p = 1, q = 1
  3. 3. tautology
  4. 4. contingency
  5. 5. N = 15
  6. 6. ∀x (A(x) ∧ ¬B(x))

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