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
pqq ↔ (p ∧ q)11100100

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

q ↔ (p ∧ q)
  1. 1p = 1, q = 1
  2. 2p = 1, q = 0
  3. 3p = 0, q = 1
  4. 4p = 0, q = 0
2.Easy
pqq ∨ p11100100

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

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 ∨ r¬q ∨ ¬r¬q ∧ ¬r¬q ∧ r

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

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

You want to prove (p ∧ q) → ¬r by contrapositive. Which implication do you prove instead? Click it.

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

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

(¬(s → r) → (¬p ∨ q)) ∧ ¬((q → ¬p) ↔ r)
N =
6.Hard
pqrr → pq → pr → q111110101100011010001000

The argument with premises r → p; q → p and conclusion r → q is invalid. Click the row of the truth table that is a counterexample.

r → pq → p∴ r → q
  1. 1p = 1, q = 1, r = 1
  2. 2p = 1, q = 1, r = 0
  3. 3p = 1, q = 0, r = 1
  4. 4p = 1, q = 0, r = 0
  5. 5p = 0, q = 1, r = 1
  6. 6p = 0, q = 1, r = 0
  7. 7p = 0, q = 0, r = 1
  8. 8p = 0, q = 0, r = 0

Answer key

  1. 1. p = 0, q = 1
  2. 2. p = 0, q = 0
  3. 3. ¬q ∨ ¬r
  4. 4. ¬¬r → ¬(p ∧ q)
  5. 5. N = 7
  6. 6. p = 1, q = 0, r = 1

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