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¬p → (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
2.Easy

How many rows N does the complete truth table of (¬(r → ¬q) ∨ p) ∨ ¬(r ∧ (p ∨ q)) have?

(¬(r → ¬q) ∨ p) ∨ ¬(r ∧ (p ∨ q))
N =
3.Medium
b ∧ ¬a¬b ∧ a¬b ∨ ¬ab → ¬a

Which formula is logically equivalent to ¬(b → a)? Click it.

¬(b → a)
  1. 1b ∧ ¬a
  2. 2¬b ∧ a
  3. 3¬b ∨ ¬a
  4. 4b → ¬a
4.Medium
pqr¬p¬q → ¬p¬((¬r → q) ∧ r) ∧ (¬q → ¬p)111?110?101?100?011?010?001?000?

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

¬((¬r → q) ∧ r) ∧ (¬q → ¬p)
N =
5.Hard

How many of the 16 rows of the truth table make (¬(a ∧ c) ∨ ¬d) ∧ ((a ∧ c) ∨ b) true? Call this number N.

(¬(a ∧ c) ∨ ¬d) ∧ ((a ∧ c) ∨ b)
N =
6.Hard
aca ∨ ca¬c11100100

The argument with premises a ∨ c; a and conclusion ¬c is invalid. Click the row of the truth table that is a counterexample.

a ∨ ca∴ ¬c
  1. 1a = 1, c = 1
  2. 2a = 1, c = 0
  3. 3a = 0, c = 1
  4. 4a = 0, c = 0

Answer key

  1. 1. p = 0, q = 1
  2. 2. N = 8
  3. 3. b ∧ ¬a
  4. 4. N = 3
  5. 5. N = 8
  6. 6. a = 1, c = 1

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