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
ab(b → a) ∧ ¬a11100100

Exactly one row of the truth table makes (b → a) ∧ ¬a true. Click that row.

(b → a) ∧ ¬a
  1. 1a = 1, b = 1
  2. 2a = 1, b = 0
  3. 3a = 0, b = 1
  4. 4a = 0, b = 0
2.Easy
pqp ∧ ¬q11?10?01?00?

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

p ∧ ¬q
N =
3.Medium
tautologycontradictioncontingency

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

((p ∨ q) ∧ p) → ¬q
  1. 1tautology
  2. 2contradiction
  3. 3contingency
4.Medium
¬a ∧ ¬c¬a ∧ c¬a ∨ ¬c¬a ∨ c

Which formula is logically equivalent to ¬(a ∧ c)? Click it.

¬(a ∧ c)
  1. 1¬a ∧ ¬c
  2. 2¬a ∧ c
  3. 3¬a ∨ ¬c
  4. 4¬a ∨ c
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 ¬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. a = 0, b = 0
  2. 2. N = 1
  3. 3. contingency
  4. 4. ¬a ∨ ¬c
  5. 5. ∀x (F(x) → ¬G(x))
  6. 6. ∃x ¬A(x)

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