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
abb → a11?10?01?00?

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

b → a
N =
2.Easy
abb → (a ↔ b)11100100

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

b → (a ↔ b)
  1. 1a = 1, b = 1
  2. 2a = 1, b = 0
  3. 3a = 0, b = 1
  4. 4a = 0, b = 0
3.Medium
¬r → ¬qr → q¬r ∧ ¬q¬q → ¬r

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

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

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

q → (q ∧ r)
  1. 1tautology
  2. 2contradiction
  3. 3contingency
5.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))
6.Hard
r¬p ∧ rp¬p

The premises p → r; ¬r are given. Which conclusion follows from them? Click it.

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

Answer key

  1. 1. N = 3
  2. 2. a = 0, b = 1
  3. 3. ¬r → ¬q
  4. 4. contingency
  5. 5. ∀x (A(x) ∧ ¬B(x))
  6. 6. ¬p

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