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

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

(p → q) ∨ (¬r ∧ p)
N =
2.Easy
ab¬((a ∨ 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
(p ∧ q) ∧ ¬r¬(p ∧ q) ∧ ¬r¬(p ∧ q) → ¬r¬(p ∧ q) ∧ r

You want to prove (p ∧ q) → r by contradiction. Which statement do you assume at the start? Click it.

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

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

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

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

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

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

¬(b → c) ∧ ((d ↔ b) ↔ (c ∧ a))
N =

Answer key

  1. 1. N = 7
  2. 2. a = 0, b = 1
  3. 3. (p ∧ q) ∧ ¬r
  4. 4. (r ∨ q) ∧ (r ∨ p)
  5. 5. N = 14
  6. 6. N = 2

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