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
pqp → ¬q11?10?01?00?

Complete the truth table (1 = true, 0 = false). In how many rows N is p → ¬q true?

p → ¬q
N =
3.Medium
(r ∧ p) ∨ qr ∨ (p ∧ q)(r ∧ p) ∨ (r ∧ q)(r ∨ p) ∧ (r ∨ q)

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

r ∧ (p ∨ q)
  1. 1(r ∧ p) ∨ q
  2. 2r ∨ (p ∧ q)
  3. 3(r ∧ p) ∨ (r ∧ q)
  4. 4(r ∨ p) ∧ (r ∨ q)
4.Medium
¬b ∨ a¬b ∧ a¬b ∨ ¬a¬b ∧ ¬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. 4¬b ∧ ¬a
5.Hard
acc → aac11100100

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

c → aa∴ c
  1. 1a = 1, c = 1
  2. 2a = 1, c = 0
  3. 3a = 0, c = 1
  4. 4a = 0, c = 0
6.Hard

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

((r → s) ∧ p) ∧ ((q ∨ ¬s) → q)
N =

Answer key

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

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