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
pqq ∨ (q ↔ p)11?10?01?00?

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

q ∨ (q ↔ p)
N =
2.Easy
pqr(¬q ∨ p) ↔ r111?110?101?100?011?010?001?000?

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

(¬q ∨ p) ↔ r
N =
3.Medium
¬q ∧ pq ∨ ¬p¬q ∧ ¬p¬q ∨ ¬p

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

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

Which formula is logically equivalent to q → p? Click it.

q → p
  1. 1p → q
  2. 2¬p ∧ ¬q
  3. 3¬q → ¬p
  4. 4¬p → ¬q
5.Hard
pqq → p¬q¬p11100100

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

q → p¬q∴ ¬p
  1. 1p = 1, q = 1
  2. 2p = 1, q = 0
  3. 3p = 0, q = 1
  4. 4p = 0, q = 0
6.Hard

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

(s ∧ (q ∨ p)) ∧ (¬r ∧ ¬(¬q ∧ p))
N =

Answer key

  1. 1. N = 3
  2. 2. N = 4
  3. 3. ¬q ∧ ¬p
  4. 4. ¬p → ¬q
  5. 5. p = 1, q = 0
  6. 6. N = 2

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