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
pqp → ¬q11100100

Exactly one row of the truth table makes p → ¬q false. Click that row.

p → ¬q
  1. 1p = 1, q = 1
  2. 2p = 1, q = 0
  3. 3p = 0, q = 1
  4. 4p = 0, q = 0
2.Easy
pqr¬(p → (¬r ∨ q))111?110?101?100?011?010?001?000?

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

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

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

(¬r ↔ ¬p) ∧ (¬(p → q) → (¬r → q))
N =
4.Medium
b → ¬a¬b ∨ ¬ab ∧ ¬a¬b ∧ a

Which formula is logically equivalent to ¬(b → a)? Click it.

¬(b → a)
  1. 1b → ¬a
  2. 2¬b ∨ ¬a
  3. 3b ∧ ¬a
  4. 4¬b ∧ a
5.Hard
∀x F(x)∃x F(x)∀x ¬F(x)∃x ¬F(x)

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

¬∀x F(x)
  1. 1∀x F(x)
  2. 2∃x F(x)
  3. 3∀x ¬F(x)
  4. 4∃x ¬F(x)
6.Hard
qrq → r¬q¬r11100100

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

q → r¬q∴ ¬r
  1. 1q = 1, r = 1
  2. 2q = 1, r = 0
  3. 3q = 0, r = 1
  4. 4q = 0, r = 0

Answer key

  1. 1. p = 1, q = 1
  2. 2. N = 1
  3. 3. N = 4
  4. 4. b ∧ ¬a
  5. 5. ∃x ¬F(x)
  6. 6. q = 0, r = 1

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