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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
pqq ↔ ¬(p → q)11100100

Exactly one row of the truth table makes q ↔ ¬(p → q) true. Click that row.

q ↔ ¬(p → q)
  1. 1p = 1, q = 1
  2. 2p = 1, q = 0
  3. 3p = 0, q = 1
  4. 4p = 0, q = 0
2.Easy
pq(p → q) ∧ q11?10?01?00?

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

(p → q) ∧ q
N =
3.Medium
¬¬c → ¬¬a¬¬c ∧ ¬¬a¬¬c ∧ ¬a¬c ∧ ¬¬a

You want to prove ¬c → ¬a by contradiction. Which statement do you assume at the start? Click it.

¬c → ¬a
  1. 1¬¬c → ¬¬a
  2. 2¬¬c ∧ ¬¬a
  3. 3¬¬c ∧ ¬a
  4. 4¬c ∧ ¬¬a
4.Medium
pqr(¬r ∧ ¬q) ↔ p(r ∨ q) → ((¬r ∧ ¬q) ↔ p)¬((r ∨ q) → ((¬r ∧ ¬q) ↔ p))111?110?101?100?011?010?001?000?

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

¬((r ∨ q) → ((¬r ∧ ¬q) ↔ p))
N =
5.Hard
∃x (¬A(x) ∨ ¬B(x))∀x (¬A(x) ∧ ¬B(x))∀x (¬A(x) ∨ ¬B(x))∃x (¬A(x) ∧ ¬B(x))

Which statement is equivalent to ¬∀x (A(x) ∨ B(x)), with the negation moved all the way inside? Click it.

¬∀x (A(x) ∨ B(x))
  1. 1∃x (¬A(x) ∨ ¬B(x))
  2. 2∀x (¬A(x) ∧ ¬B(x))
  3. 3∀x (¬A(x) ∨ ¬B(x))
  4. 4∃x (¬A(x) ∧ ¬B(x))
6.Hard
a → c¬a → ¬cc → aa ∧ c

The premises a → b; b → c are given. Which conclusion follows from them? Click it.

a → bb → c
  1. 1a → c
  2. 2¬a → ¬c
  3. 3c → a
  4. 4a ∧ c

Answer key

  1. 1. p = 0, q = 0
  2. 2. N = 2
  3. 3. ¬c ∧ ¬¬a
  4. 4. N = 3
  5. 5. ∃x (¬A(x) ∧ ¬B(x))
  6. 6. a → c

Full step-by-step solutions: practise this topic on examproblems.com.