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
pq(q ↔ p) → q11100100

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
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
pqrr → (q ∨ ¬p)r ∨ q(r → (q ∨ ¬p)) ↔ (r ∨ q)111?110?101?100?011?010?001?000?

In how many of the 8 rows of its truth table is (r → (q ∨ ¬p)) ↔ (r ∨ q) true? Call this number N.

(r → (q ∨ ¬p)) ↔ (r ∨ q)
N =
4.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
5.Hard
pqrp → (q ∨ r)pq111110101100011010001000

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

p → (q ∨ r)p∴ 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
6.Hard

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

((q ↔ s) ∧ p) ∧ ((¬r ∨ q) ∨ (r → p))
N =

Answer key

  1. 1. p = 0, q = 0
  2. 2. a = 0, b = 1
  3. 3. N = 5
  4. 4. b ∧ ¬a
  5. 5. p = 1, q = 0, r = 1
  6. 6. N = 4

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