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
abc(c ∨ a) ∨ ((b → c) ∨ a)111110101100011010001000

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

(c ∨ a) ∨ ((b → c) ∨ a)
  1. 1a = 1, b = 1, c = 1
  2. 2a = 1, b = 1, c = 0
  3. 3a = 1, b = 0, c = 1
  4. 4a = 1, b = 0, c = 0
  5. 5a = 0, b = 1, c = 1
  6. 6a = 0, b = 1, c = 0
  7. 7a = 0, b = 0, c = 1
  8. 8a = 0, b = 0, c = 0
3.Medium
(q → p) ∧ (¬p → ¬q)q ∧ p(q → p) ∧ (p → q)(q → p) ∨ (p → q)

Which formula is logically equivalent to q ↔ p? Click it.

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

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

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

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

((p → q) ∧ p) ∧ (¬(¬r ∨ ¬s) → (q ∨ s))
N =
6.Hard

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

(s ∧ (p ∨ q)) ∨ ((¬r → s) ↔ r)
N =

Answer key

  1. 1. p = 0, q = 0
  2. 2. a = 0, b = 1, c = 0
  3. 3. (q → p) ∧ (p → q)
  4. 4. ¬q ∧ ¬p
  5. 5. N = 4
  6. 6. N = 15

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