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
pqp → q11100100

Exactly one row of the truth table makes p → q false. Click that row.

p → q
  1. 1p = 1, q = 1
  2. 2p = 1, q = 0
  3. 3p = 0, q = 1
  4. 4p = 0, q = 0
2.Easy
aba ∨ ¬(b → a)11100100

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

a ∨ ¬(b → a)
  1. 1a = 1, b = 1
  2. 2a = 1, b = 0
  3. 3a = 0, b = 1
  4. 4a = 0, b = 0
3.Medium
¬b → ¬a¬b ∧ a¬b ∨ ¬ab ∧ ¬a

Which formula is logically equivalent to ¬(b → a)? Click it.

¬(b → a)
  1. 1¬b → ¬a
  2. 2¬b ∧ a
  3. 3¬b ∨ ¬a
  4. 4b ∧ ¬a
4.Medium
(r ∨ p) ∧ qr ∧ (p ∨ q)(r ∧ p) ∨ (r ∧ q)(r ∨ p) ∧ (r ∨ q)

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

r ∨ (p ∧ q)
  1. 1(r ∨ p) ∧ q
  2. 2r ∧ (p ∨ q)
  3. 3(r ∧ p) ∨ (r ∧ q)
  4. 4(r ∨ p) ∧ (r ∨ q)
5.Hard
a ∧ c¬ab ∨ ca ∨ c

The premises b ∨ a; ¬b ∨ c are given. Which conclusion follows from them? Click it.

b ∨ a¬b ∨ c
  1. 1a ∧ c
  2. 2¬a
  3. 3b ∨ c
  4. 4a ∨ c
6.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))

Answer key

  1. 1. p = 1, q = 0
  2. 2. a = 0, b = 0
  3. 3. b ∧ ¬a
  4. 4. (r ∨ p) ∧ (r ∨ q)
  5. 5. a ∨ c
  6. 6. ∃x (F(x) ∧ ¬G(x))

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