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
ab(a → ¬b) ∨ ¬a11100100

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
2.Easy

The complete truth table of ((¬c ∨ a) → ¬c) ∧ ¬(a → b) is written out. In how many rows N is a = 1 and b = 0?

((¬c ∨ a) → ¬c) ∧ ¬(a → b)
N =
3.Medium
r ∨ (p ∧ q)(r ∧ 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. 1r ∨ (p ∧ q)
  2. 2(r ∧ p) ∨ q
  3. 3(r ∨ p) ∧ (r ∨ q)
  4. 4(r ∧ p) ∨ (r ∧ q)
4.Medium
(b ∨ c) ∧ (b ∨ a)(b ∧ c) ∨ a(b ∧ c) ∨ (b ∧ a)b ∨ (c ∧ a)

Which formula is logically equivalent to b ∧ (c ∨ a)? Click it.

b ∧ (c ∨ a)
  1. 1(b ∨ c) ∧ (b ∨ a)
  2. 2(b ∧ c) ∨ a
  3. 3(b ∧ c) ∨ (b ∧ a)
  4. 4b ∨ (c ∧ a)
5.Hard

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

¬((¬d → b) → ¬(a ∨ c)) → (¬c ∧ (¬b ∧ d))
N =
6.Hard
¬prp ∧ ¬r¬r

The premises p → r; p are given. Which conclusion follows from them? Click it.

p → rp
  1. 1¬p
  2. 2r
  3. 3p ∧ ¬r
  4. 4¬r

Answer key

  1. 1. a = 1, b = 1
  2. 2. N = 2
  3. 3. (r ∧ p) ∨ (r ∧ q)
  4. 4. (b ∧ c) ∨ (b ∧ a)
  5. 5. N = 8
  6. 6. r

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