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(a → ¬b) → (¬b → a)11100100

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

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

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

p → (q ↔ p)
  1. 1p = 1, q = 1
  2. 2p = 1, q = 0
  3. 3p = 0, q = 1
  4. 4p = 0, q = 0
3.Medium
¬q ∧ ¬(p ∨ r)q ∧ ¬(p ∨ r)¬q → ¬(p ∨ r)¬q ∧ (p ∨ r)

You want to prove q → (p ∨ r) by contradiction. Which statement do you assume at the start? Click it.

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

You want to prove q → (r ∧ p) by contradiction. Which statement do you assume at the start? Click it.

q → (r ∧ p)
  1. 1¬q ∧ ¬(r ∧ p)
  2. 2q ∧ ¬(r ∧ p)
  3. 3¬q ∧ (r ∧ p)
  4. 4¬q → ¬(r ∧ p)
5.Hard

How many of the 16 rows of the truth table make ¬(((q ↔ p) ∨ (r ∨ ¬s)) ∨ (r ∧ ¬q)) true? Call this number N.

¬(((q ↔ p) ∨ (r ∨ ¬s)) ∨ (r ∧ ¬q))
N =
6.Hard
∃x ¬F(x)∀x ¬F(x)∀x F(x)∃x F(x)

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

¬∃x F(x)
  1. 1∃x ¬F(x)
  2. 2∀x ¬F(x)
  3. 3∀x F(x)
  4. 4∃x F(x)

Answer key

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

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