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
pq(q ↔ ¬p) → ¬q11?10?01?00?

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

(q ↔ ¬p) → ¬q
N =
2.Easy
pqq ∧ p11?10?01?00?

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

q ∧ p
N =
3.Medium
(q ∧ p) ∨ rq ∨ (p ∧ r)(q ∨ p) ∧ (q ∨ r)(q ∧ p) ∨ (q ∧ r)

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

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

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

r → p
  1. 1¬p → ¬r
  2. 2p → r
  3. 3¬r → ¬p
  4. 4¬p ∧ ¬r
5.Hard

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

(r ∧ (q → s)) → ((p → r) ∧ (s → p))
N =
6.Hard
prr → ppr11100100

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

r → pp∴ r
  1. 1p = 1, r = 1
  2. 2p = 1, r = 0
  3. 3p = 0, r = 1
  4. 4p = 0, r = 0

Answer key

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

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