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

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

(¬q ∧ (p ∧ r)) → ¬(r ∨ (¬p → ¬q))
N =
2.Easy
ab(¬b ∧ a) ∨ (b ↔ a)11?10?01?00?

Complete the truth table (1 = true, 0 = false). In how many rows N is (¬b ∧ a) ∨ (b ↔ a) true?

(¬b ∧ a) ∨ (b ↔ a)
N =
3.Medium
abca ∧ cc → (a ∧ c)((a ∧ b) → b) ↔ (c → (a ∧ c))111?110?101?100?011?010?001?000?

In how many of the 8 rows of its truth table is ((a ∧ b) → b) ↔ (c → (a ∧ c)) true? Call this number N.

((a ∧ b) → b) ↔ (c → (a ∧ c))
N =
4.Medium
pqr¬r¬q ∨ ¬r(¬(p → r) ∨ (q ∧ p)) ∧ (¬q ∨ ¬r)111?110?101?100?011?010?001?000?

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

(¬(p → r) ∨ (q ∧ p)) ∧ (¬q ∨ ¬r)
N =
5.Hard
prp → rrp11100100

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

p → rr∴ p
  1. 1p = 1, r = 1
  2. 2p = 1, r = 0
  3. 3p = 0, r = 1
  4. 4p = 0, r = 0
6.Hard
abcc → (b ∨ a)cb111110101100011010001000

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

c → (b ∨ a)c∴ b
  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

Answer key

  1. 1. N = 2
  2. 2. N = 3
  3. 3. N = 6
  4. 4. N = 2
  5. 5. p = 0, r = 1
  6. 6. a = 1, b = 0, c = 1

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