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¬(p ∧ (p ↔ q))11?10?01?00?

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

¬(p ∧ (p ↔ q))
N =
2.Easy

How many rows N does the complete truth table of ¬(a → b) ↔ (c → a) have?

¬(a → b) ↔ (c → a)
N =
3.Medium
(b ∧ a) ∨ (b ∧ c)(b ∧ a) ∨ c(b ∨ a) ∧ (b ∨ c)b ∨ (a ∧ c)

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

b ∧ (a ∨ c)
  1. 1(b ∧ a) ∨ (b ∧ c)
  2. 2(b ∧ a) ∨ c
  3. 3(b ∨ a) ∧ (b ∨ c)
  4. 4b ∨ (a ∧ c)
4.Medium
abc¬a¬a ∨ c(b ↔ c) ∧ (¬a ∨ c)111?110?101?100?011?010?001?000?

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

(b ↔ c) ∧ (¬a ∨ c)
N =
5.Hard

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

((q → ¬r) ↔ s) ↔ (p ∧ (r → ¬p))
N =
6.Hard
pqrq → rp → rq → p111110101100011010001000

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

q → rp → r∴ q → p
  1. 1p = 1, q = 1, r = 1
  2. 2p = 1, q = 1, r = 0
  3. 3p = 1, q = 0, r = 1
  4. 4p = 1, q = 0, r = 0
  5. 5p = 0, q = 1, r = 1
  6. 6p = 0, q = 1, r = 0
  7. 7p = 0, q = 0, r = 1
  8. 8p = 0, q = 0, r = 0

Answer key

  1. 1. N = 3
  2. 2. N = 8
  3. 3. (b ∧ a) ∨ (b ∧ c)
  4. 4. N = 3
  5. 5. N = 8
  6. 6. p = 0, q = 1, r = 1

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